In my game there’s a Ranger who is a demigod and doesn’t know it (my homebrew, but shouldn’t affect the question I have). He has a pet “lizard” who is actually a polymorphed Deva in disguise that his father sent to keep tabs on him. The Deva is using his innate polymorphing ability.

The player is planning on taking the Beast Master Archetype and wants to choose his pet “Gecky” the “lizard” as his ranger companion. Would “Gecky” count as a Beast for the purpose of bonding if he’s already spent years in polymorphed form watching over him, or would bonding fail due to his being of the Celestial type?

What's important to you here, the fluff or the crunch?

"Fluff" is the game world that the DM describes and the players interacts with. "Crunch" is the actual game rules mechanics. For example, if you had a player who described their character as a lightly armored duelist fighter who specialized in the rapier, that's their fluff, while the crunch might be that they're actually using the rogue class rather than the fighter class.

If the fluff of this pet being a deva watching over the ranger is what's important to you, then sure, it works fine. Use the lizard crunch at all times for the pet, so the ranger doesn't gain non-standard mechanical benefits. Treat it mechanically as if the ranger had chosen some other perfectly normal lizard, and just focus on the story implications.

If the crunch of this lizard being a deva is what's important, i.e. that if push comes to shove it can actually bust out some Angel Awesomeness™, then no, it cannot be chosen as the ranger's beast companion. As mentioned in other answers, the deva's polymorph explicitly says it keeps its regular stats, as compared to the druid's wildshape which explicitly gives beast stats. You'll need to think about how the player might react to their attempt to make this lizard their beast companion, and how the deva might respond to those reactions.

To clarify, you should be OK as long as you keep the crunch consistent. It doesn't really matter whether you use the game rules for a lizard or for a deva, as long as you don't try to mix and match the two sets of rules.

No, it can't bond with a shapechanged deva

The deva's Change Shape action says:

In a new form, the deva retains its game statistics and ability to speak, but its AC, movement modes, Strength, Dexterity, and special senses are replaced by those of the new form, and it gains any statistics and capabilities (except class features, legendary actions, and lair actions) that the new form has but that it lacks.

Nowhere here does it say it changes the creature type of the Deva, so it is still a Celestial; i.e. not applicable for Beast Companion. For example, the Druid's Wild Shape says:

Your game statistics are replaced by the statistics of the beast

...which expressly states that the Druid becomes a beast. In addition, as @fabian mentioned, a Deva is not CR $frac14$ or lower.

Purely rules-as-written, no, you can't do this; a Deva's polymorph doesn't give them the ability to change their type. A ranger gets a beast companion, not a celestial.

But assuming you want to hand-wave that and just say "a god did it, it's fine", then you're off in the weeds, and the answer to this is going to ultimately be that it's up to the DM. (I'm uncertain whether that's you or not.) For a thing like this, the player should work with the DM to figure out what's going on and how it operates, and as much as I hate to give this kind of answer, it doesn't matter unless it matters.

For example, I'm not sure why you chose a Deva in specific. Just because they have a polymorph power? It could just as easily be a "celestial spirit" in lizard form, which isn't explicitly an angel of any type -- the same kind of thing you could get from a Find Familiar spell could be in play here.

If the being is constrained to stay in beast-form at all times, and has the stats of a beast, then there's no real problem; it's just a companion animal like any other with a small twist. Having a different type than usual isn't a huge deal.

But is the expectation for the companion to have the stats of a Deva, with resistance to weapon damage and a three-digit HP total? Having a virtually invincible animal companion is obviously not balanced, so there's an issue there.

Is the player expecting that if the Ranger goes down and is about to die, his secret angel buddy is gonna suddenly pop their wings so they can save the Ranger with a healing touch, and maybe strike down upon the enemy with great vengeance and furious anger?

Because, I mean, the DM can do that if they want -- honestly that would probably make a pretty awesome pre-planned story beat when everything gets revealed, and then the angel buddy has to go back to the planes, because they broke the rules. But a cool story moment shouldn't have to be prefaced with months of gaming with a mechanically broken party member.

My recommendation is to forget the word 'deva' entirely for now, and have it just have the usual lizard stats in every way (except, possibly, the type). You'll need to have a plan for what's going to happen if the lizard drops to zero hit points or if it dies, and what it's going to do if the Ranger is in serious danger of death. If one of those plans says something like "the lizard turns into an angel", that's totally fine; don't feel like you need to mechanically justify how it was able to do that.

Ditch the rules saying "can do" or "can not" and go for it.

Reasoning: There are no demigod rules and your homebrew do affect the answer. If you go straight RAW, the premise of having a demigod as a PC is violated because of that. Therefore, you should do for the deva-disguised-as-lizard the same as your demigod-disguised-as-ranger:

Just use the normal rules for {Ranger} and {Lizard companion} until the big reveal. Revert to (extra-) ordinary game statistics for the real deal afterwards.

RPG is about telling a story. The game rules exist for gamifying that. The informal rules called Golden Rule and the Rule of Awesome are your friends here.

One caveat: After the big reveal, control of the lizard-that-was-a-deva-all-this-time should not remain with the player. Also make sure none of the other players get angry or envious of the demigod status this one earned. Counterbalance with lots of trouble as one would in a novel.

You’re the DM. It’s ultimately up to you. The DMG, Monster Manual, all the rule books are just a guide. You get to choose how to use them. Try your angel in disguise thing and see how it all turns out. Get creative with making your own rules. Etc. Just make sure your party knows everything they need to know without ruining the story.