Wizards only as Liches?

I am in the process of world building for a new game. My ultimate big bad is going to be a lich, but the bit of research I have done so far all refers to liches having to be wizards, due to the spell and phylactery creation requirement.

So I guess my question is this: could a non-magic user become a lich, assuming he could convince a mage to perform the rites?