A wobbling pulsar will do the trick.

Pulsars emit a lot of energy in narrow beams that come from their poles. The slowest ones flash every few seconds; make its tilt wobble so that it is not pointing at the planet all the time. In addition, wobbling causes the pulsar to shoot at different points of the planet's orbit through time. The planet is hit when the pulsar's beams' path just happens to be passing by the planet.

If the pulsar is flashing every few milliseconds (as is normal for them), it will seem like a continuous beam for observers.

Finally, to make the beam small enough that it doesn't cover the entire planet and more, justify it with lensing from nearby nebulas, the planet's atmosphere, and maybe a black hole between the pulsar and the planet.

The remains of an ancient Dyson swarm

Not quite natural, but mostly non-technological. If a prior civilization had constructed a Dyson swarm around the system's star, the light coming from the star might be heavily occluded. Assume the sun is >10X hotter than ours (or the planet is much closer in), and there are enough collector bodies in the swarm to block some 90% of the sun's light at any time. If they are close enough in toward the sun, there will be enough diffraction around each collector that they wouldn't cast visible shadows, and could only be observed by direct observation of the sun, which requires a minimum level of technology to avoid blinding yourself.

The spotlight effect would occur when resonances in the orbital periods of the different bodies in the swarm cause gaps in coverage. The creating civilization could have arranged this purposefully to provide sunlight to further flung planets/stations, or be coincidental. The apparent brightness would grow gradually as more pieces of the swarm leave the "hole" in the field, so the warning sign would just be a rapid but gradual increase in brightness.

The spotlight color would probably be the same as the normal sunlight. However, if the star is very hot, heading toward blue spectrum, the swarm might occlude the blue/UV portion of the spectrum more and let redder light through (imagine if each collector is a giant solar array panel with no backing, e.g. microns of silicon). At the very least they would radiate heat in the infrared. If natives to the planet are used to these conditions, that might be their normal "white" light.

Any sort of passive light-focusing (with lenses, mirrors, etc) scheme is unlikely do more than to make slightly warm spots. The fundamental reason has to do with the conservation of etendue, and you can read more about it at Would a Moon made of water pose a threat to Earth during eclipses?

As such, if you want the spotlight to come from a moon, the moon would either need some kind of power source (which starts to sound like "giant lasers") or would need some natural mechanism to eject jets of energy or matter. As far as I know, all kinds of astrophysical jets would require something much more massive than a moon, so this seems like a dead-end.

I think the most feasible explanation is a planet which is ordinarily protected by its atmosphere and/or magnetosphere, but on occasion the weather aligns such that the protection is lost in an area. We to experience this to a small extent on earth: both the sun and earth have magnetic fields that vary over time. One trouble is if the earth's magnetosphere were periodically penetrated by the solar wind, the atmosphere would be stripped away. Though it could take a very long time -- perhaps it is interesting for your story to have a "dying planet".

Not entirely sure about the feasibility of this, but it's an idea I had when I read your question. I wonder if something like this would be possible through Gravitational Lensing. Essentially, this is when black holes (with enormous gravitational pulls) bend light around them, causing telescopic effects. I've linked the Wikipedia page for gravitational lensing as well as an article from Space.com below which you could read up on to give you a better idea of how it all works.

My idea though is that what if, just outside the edge of what can be seen from the planet, there's a system of black holes which pull light in such a manner that it's focussed into a thin beam, which cuts across the galaxy and occasionally burns its way across your planet? This would explain the huge intensity of the light as well as allowing a 'natural' explanation for how it's focussed so tightly.

Having it at such a distance would also mean that the appearance of the beam of light can't be predicted, as the people on the planet don't have the technology to either see that far into space, or understand what they're seeing. Besides, at such a distance that the black holes don't mess with the solar system's structure, the light would take very long to reach the planet. So when the beam lines up, its effects are only seen on the planet later (how much later depends on the distance. Centuries, or even millennia maybe).

As for the colour of the beam, we can assume the source of light is moving away from the black holes and the planet, which would cause Redshift. This would make a white light source look red to the observer. Frequency wise, we could assume that other objects in space (planets, dust clouds etc) often block the light from hitting our planet, but occasionally it slips through the gaps (like when you see the sun for a couple of seconds through a clearing in the clouds before it gets blocked again).

For non-animals to survive, perhaps they've evolved to feed on the huge light intensity and maybe even need it every few days to live? Or (depending on the history of the 'humans' on your planet) maybe everything else is evolved to survive the intense light to an extent, while humans aren't. Perhaps this is similar to how we have to wear clothes - we can't handle Earth's natural climates without external help. Maybe those caught outside of their radiation booths are killed rapidly, while those who stay inside are fine?

There's a lot of ways you can go with this idea and I think the rest is up to you. I've included a few links at the bottom you might be interested in.

Further Reading:

Gravitational lensing:

https://www.space.com/39999-how-gravitational-lenses-work.html

https://en.wikipedia.org/wiki/Gravitational_lens

Red and blue shift:

https://en.wikipedia.org/wiki/Redshift

https://www.space.com/25732-redshift-blueshift.html

Ozone holes (https://en.wikipedia.org/wiki/Ozone_depletion) already cause real world health problems.

I think you could combine ozone holes and the loss of other atmospheric protection with the a coinciding local weakening of the magnetosphere. In the presence of a very energetic "sun", the results might be "deadly".

"Deadly" as in it might be immediately painful and certainly cancerous over time. Not deadly in the Vin Diesel kind of way you might be looking for though.

Let's have some cosmic fun.

Say that your planet orbits inside of an expanding red giant star.

Yep.

Now, say that someone or something decided to construct a shell around your world, perhaps before it had been engulfed by your host star as it evolved from the main sequence. This shell may be layers upon layers of orbital rings.

Now, say that this shell--made of some impossible material, probably--has some degree of translucency to it and the ability to change this translucency. You can have one hemisphere of the shell totally opaque to simulate night, with perhaps little points of translucency to simulate stars, and the other hemisphere translucent to simulate daylight (much less a simulation this point, because actual starlight would be entering).

Finally, let this shell have some circular region of total transparency which sweeps the planet, perhaps moving across the shell faster than the day-night cycle to give the folks on all sides, day or night, some of the action. You can think of the shell as being comprised of a bunch of little windows if you'd like, like pixels on a screen, that can be tinted and whatnot and can be made to filter out the unnecessary or harmful radiation of the star it is orbiting inside. The transparent portion would not filter these things, allowing death to beam down onto everything below. Heck, perhaps it even has little perforations or 'openings of the windows' that allow actual, high-energy particles to enter as well.

Constant lightning.

Consider a Rocheworld.
Can an atmosphere englobe a planetary ring?

Two tidally locked planets just outside the Roche Limit can orbit each
other and share a combined atmosphere. You would be able to fly from
one to the other without ever leaving the atmosphere and objects
placed at the lagrange points would be able to remain there.

These binary planets circle around each other. At one point in their orbit, their atmospheres touch (or you could have a moon graze the atmosphere of its planet). The friction of the two atmospheres against each other produces colossal amounts of electrical charge. When the two are close enough that the atmosphere can provide a path, charge can equilibrate across.

This takes the form of constant tremendous bolts of lightning that follow the path of the point where the two partners are closest to one another.

I haven't seen this directly addressed, so I'll pose it as an answer:

TL;DR: Large moon with atmosphere refracts to a "point" on your planet. See below for etendue/thermodynamics, refraction, periodicity, and "warning signs".

A companion (moon, twin planet, or even planet as primary with your story set on a comfortable moon of a gas giant) large enough to hold a substantial atmosphere can perhaps be tuned to get the result you need.

Devise an atmosphere for the companion body with a powerful thermal inversion somewhere that reduces some of the spreading due to typical refraction of a density-stratified lens.

So we effectively have a ring-shaped lens, fairly narrow (edge view of the companion's atmosphere) but of very wide diameter (the companion itself), tuned to refract fairly well to a "point". The source of the light is the sun, and we will not get hotter than that. We do not need perfect point focus, but will gladly accept a central line of foci for various degrees of refraction, which generate -- you guessed it -- different colors of spotlight at different orbital distance of the large body from your planet's surface. Blue when it's close, red when it's far -- if it behaves like a proper lens-shaped lens. This would also result in color change as the effect sweeps from the edge of the home planet (farther) to the center (a bit closer). Warning signs would be similar to normal eclipses (the effect would only be observable from the very height of the eclipse). Finally, a combination of rotational and orbital planes for the three bodies involved can do wonders for making a simple periodic set of processes appear miserably non-periodic, particularly for observers located at different points on the surface of the home body.

I'll create a graphic. But I think this thing is doable with a lot less machinery than has been proposed so far, and without violating physics to the point of ridicule.

The moon discussion referenced by @Phil Frost suggests part of the answer. A moon is too small so the lens-like body or phenomenon has to be big enough to cover all or most of the sky from the point of view of the target planet (which may itself be just a moon in a bigger system).

The problem is coming up with a celestial lens. If you can solve that, the rest is just a question of placing the target planet and the radiation source at a suitable scale and proximity.

A lens spotlight redirects light from a large area outside the "spot" so the first warning of the death ray's proximity would be a significant darkening, similar to a solar eclipse. In the distance you might see reflections from dust or clouds within the cone of concentrated light, so you can see if it's coming closer.

The system could be a binary system with a neutron star or black hole orbiting close to the main star but in an eccentric orbit that lasts a few days. When it draws close to the primary it pulls off huge masses of coronal gasses and causes massive incredibly intense solar flares. If these incidents happen at the same time as the planet is in the wrong part of the sky then you can expect some serious pyrotechnics to hit the day side of the planet for a few hours.

The black hole/neutron star would most likely have been captured rather than be an original part of the system, explaining the eccentric orbit and any unusual spin needed etc.

It doesn't take a big stretch to somehow say that the gravity and magnetic fields of the neutron star focuses the ejections into beams somehow. So every X hours you get massive beams of solar energy being fired in random directions. You can then get the variance by saying whether those beams hit your planet or not.

A small moon-like object in the planet+star's L1 Lagrange point (i.e., the point where the star's and planet's gravity exactly cancel out) would do the trick. Thanks to the wave nature of light, the moon will generate an Arago spot (bright spot) on the surface of your planet. Pick a small and bright star, perhaps a young white dwarf or neutron star.

To have a moving spot, the moon would need to move about a bit. You can think of an orbit around the L1 point. This should not be too hard.

Much more difficult is the fact that the L1 point is an unstable equilibrium point. Objects do not remain in orbit around the L1 point looking only at gravitational forces. Here, some handwaving is necessary. Perhaps the pressure from stellar winds from the central star have some stabilising influence. Perhaps heating of parts of the planets not obscured by the moon will cause massive out-gassing of the oceans into space, providing a stabilising pressure.

Regardless, it's definitely not a predictable situation, which should make it ideal for your story.

Reverse Solar Eclipse.

An orbiting Ocean, say a liquid helium moon of the correct size. Meaning, blocking the entire star, or larger. It could create a focusing and penumbra effect based on your need for destruction. Reinforce your physics.