3e also had a Deities & Demigods that provided stats for gods that could be fought and killed. However, I never played that edition and I may be missing something. As far as I can tell this are the actual god stats not avatars.
You are indeed missing something.
The whole book is an "DM's Option" book, essentially, full of choices (and hilariously dumb statblocks which just express everything that was messed-up about 3E). The book has a section at the end about whether gods can die, and it really notes the problems with letting them die, and notes that them
not (normally - i.e. outside of a Time of Troubles-type situation) being able to die makes a lot more sense. On top of that the statblocks for any kind of "serious" god are so insane (and their immunities so complete, and spellcasting abilities so vast), that literally only cheats or maybe other gods could kill them (even in the statblock sense - even other gods would have to "chip damage" them down over dozens of rounds, it would be a monumentally boring fight). PCs never could without extensive cheating/Monty Haul'ing/kobold railguns etc.
4e provided stats for several gods. The even gave descriptions on what was need to actually kill a god (more than just a statblock). There was even an adventure path that ended with killing Tiamat in her lair (with options to make a permanent death or not). All the gods stats also had lesser avatar versions called "Aspects."
Where are these "stats for several gods" in 4E? I'm looking through my 4E books and I'm seeing nothing but Tiamat. Though at least you're saying they couldn't just be killed with the statblock.
It seems clear that lesser gods can attacked and possibly killed by mortals.
No? "Encountered" doesn't mean "can be killed". It never has. That's a deeply anti-logical interpretation.
Also, we can see even from that definition, some extreme inconsistencies, like Lolth being listed as a "Lesser" god (3E for example has her as intermediate, basically greater under that definition, which makes sense given her vast number of worshippers).
It's just part of the whole creepy "back to 1E vibes" bollocks that early 5E (and the appallingly-written and underbaked DMG) had, the same ones that gave us the wildly racist take on Orcs or Vistani. See how the "enemy" races have gods that are "lesser" (uh oh) no matter how numerous and powerful those enemies are (Lolth being a prime example).
