What do you do if you are called out to replace a fixture (no permit-just replacing light) and it doesn't have a UL listing? It is an antique made out of wood that was just rebuilt by either a lighting store or antique store. Do I just hang it, and if anything were to ever happen, point my finger at them?

Are lights required to be listed?

It looks like it's not a requirement in NEC 110.2, the Fine Print Note leads us to definition of Approved". Acceptable to the authority having jurisdiction.
The inspector's call?

You got it, Electure. Approved.

Sorry, I should have been clearer. That's kind of what I meant by no permit, no inspection. How can it be approved by AHJ when he/she isn't involved? What is the best way to handle this? I mention UL because around here that is what most AHJ's rely on to approve. Well, UL CSA..... and I think there's one more I don't remember off the top of my head.

DOes the work you are doing require a permit in the area?
If yes, pull the permit and ask the inspector to review the fixture in question.
If not, it's your call on what you do.