I'm pretty certain the Mantis eggs I need are in there but I can't find a key to unlock the cavren door. Where is it?

Keep exploring - you'll find a keycard to unlock it.

Also, I think you might be able to unlock it from the overseer's terminal.

You cannot unlock it from the Overseer's Office: You can click unlock cavern access but it then says "Error: Override engaged at door site."

Ah yes. I believe the key is on the same level, just down another hallway from the door out to the cavern. But I honestly can't remember.

its in one of the dorms

on a shelf to your right as you enter

Is this the jungle vault?Sorry am not sure but if so use the elevator and go to the pest control room once your out of the elevator make a left up the stairs and continue from there u should find a cave. again i'am sorry if this is the wrong vault

yes thats the vault (full of plants and mantis)

using the elevator makes no difference, its on the living/rec level, opposite side to the pool table room/canteen