[Varyon]

I think "lich" is sufficiently associated with "skeletal spellcaster" at this point that using the term for something else is just going to cause confusion for your players. Now, this could be on purpose on your part, if the characters would also be confused to see a "lich" that looks like a human in their prime, but honestly you either have a situation where this is the only type of lich that exists (in which case the characters wouldn't be surprised) or liches are also known in the setting as skeletal spellcasters, in which case characters in the setting wouldn't call this a lich. Certainly, the character could claim to be a lich to throw people off, but this wouldn't be any different from any type of immortal (or "immortal" for, say, a necromancer making liberal use of Steal Youth) making such a claim, aside from maybe the character honestly believing him/herself to be a lich due to similarities between the spells.

There's also the fact that this one is arguably a bit too fragile for the term lich to apply. Liches are typically difficult - or at least tricky - to kill, but yours is basically a robot made of meat and bone, more like an intelligent flesh golem. (EDIT: This comment is with regards to your first template)

I'd suggest a different term; revenant is always easy to match with some sort of undead, but something else may work better.

EDIT: What is the Trigger on Unkillable on the second template meant to do? Typically, Trigger means the ability doesn't work at all without the initiating Trigger, and only works for a short time thereafter, implying your Lich is as fragile as a flesh golem except for shortly after the sun sets. If the intent is instead that the character only heals at night, your Regeneration already has that covered; the character isn't going to heal more than maybe 10% HP between death and dusk (depending on when he/she died, and when the GM has you check for daily healing), but once the sun sets is going to be back up within a couple of hours.