Is lipoma usually painful? Any other thoughts of a painful movable cyst/tumor?

It depends on where it is located and how deep the fatty cyst is. I had one removed that was on my abdomen, it was quite deep and bigger than the surgeon anticipated. But, it didn't really hurt too much. Each of us have our own level of pain tolerance. As a rule, any surgical incision that is located more to the center of the body ( the nerve endings towards the center of the body are overlapped or doubled up),and if it near a bony prominence ( shoulder blade, hip bone etc.), it can tend to more uncomfortable because there is less meat/tissue over bony areas. Sense the lipoma is already painful then once it is removed and healed, the pain that you are now having will go away.