does rimmel lipstick contain pig fat?

No, I don't think it does

Just glancing at ingredients for their matte lipstick, didn't see anything that I'm certain is derived from pig or cow fat, though that doesn't mean there isn't something in there I missed. It does have sheep grease and ground up bugs, if that interests you.

you'll have to ask the maker via their website to be sure. my belief is "no" -- because using an organic product like that would attract animals and/or allow it to turn rancid -- neither of which is a good outcome for lipstick