Or rather, how to properly clean and season one. I've had one for years and I had a bunch of pulled bullets sitting in it since I was a kid. I'm not worried about any lead dust from the bullets (it's pewter after all), as I wiped the inside out with a bit soapy water and a paper towel. So how do I properly maintain it for drinking purposes?

I don't think you really have to do anything, but someone with more knowledge may be along directly.

If it is a old mug, get one of the lead test kits from homedepot or lowes $10-$12. Rub the inside of the mug with the test rag. If it turns black, there is a lot of lead in it. Acidic drinks will leach out the lead in the pewter
I even check old crockware. There are glazes that contain a lot of lead.

I am not a lead expert. I get certified by the State for Renovate/Repair every 5 years for my job at a General Contractor.

The mug is only about 15 or 20 years old. I got it at a Ren fair when I was a kid. I remember it having directions about seasoning it on a tag, but I don't know where they went. Google has led to a LOT of different answers.