The lid was firmly stuck on one of my tubes of oil paint. I tried using turps and brute strength to get it off but neither worked. In the end I got the lid off by repeated soaking upside down in a jar of 'Incredible Brush Cleaner', by Chroma, and in between soakings scraping away layers of paint with a pointed metal tool (I think it's an etching tool). This stuff also gets old paint out of brushes.
I've also heard that using heat can loosen the paint enough to get the lid off.