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They can make the magic item required to become a lich, but they have no way to use it.
Well, maybe a good UMD check could get around that.
I'm all for workarounds, but this doesn't work right out of the box.
It works perfectly fine. All the phylactery does is create a new body for the lich after the lich is killed. Outsiders can be resurrected just fine (it just requirestrue resurrection, which creates a new body just like the liches phylactery does.
Not to mention that the process of becoming a lich makes the outsider turn into an undead. It is no longer an outsider, so the oustider type rules no longer apply. The creature's soul is no longer one with the body (like it is with normal outsiders), as it has been removed and placed into a little box.
The template can be applied to any living creature. If outsiders could not be liches than an exception would be made, and it would instead say "any living creature (except outsiders)".
Pathfinder outsiders can be liches just fine. Especially in this case, as ifrits are native outsiders, not true outsiders.