
tsuruki |

Actually it doesnt :S
Outsiders have no split between the body and soul, if an outsider dies then technikly the body becomes unusable, there is no soul receptacle as there is nowhere to put the soul, the body was the soul, which is why Demon/Angel deaths are so appropriately depicted as them burning up literally.
Furthermore, the key principle of lichdom is seperating the body and soul, which is impossible for an outsider.
Final note: "Native" outsiders are an exeption to many rules that apply to outsiders and blur the lines between creature types. Aashimars and Tieflings and eemental kin are all valid Lich choices in my opinion.
Of course, none of this is Raw nor is it established as Rai, so theres nothign stopping you as GM to make this call, but there might be some players that would call b!@&!@~+ on this, so make sure you hint at this beforehand so that youre not stuck with "Its my world and I do what I want" as an excuse afterwards.

wraithstrike |

Liches can not be outsiders per RAW because they are one unit. That is why even in 3.5 they had to have special liches when used with outsiders. the idea is that the soul lies in the phylactery and when the body dies the phylactery reforms the body, but outsiders can do this because the soul is the body.