How to remove makeup stain from fabric lining ?

If you do a search on make up stain, there are a variety of recommendations from micellar water to making a paste of . . . But, I think many of these are for leather linings.
also, I would take it to a trusted dry cleaner or bag specialist before attempting home remedies Depending on the value of the bag and your tolerance risk (mine is actually relatively high)
for a prestige brand, you can also try doing a search in the individual designer forum.
Good luck!