I have what feels like a fatty lump that moves easily under my skin on the right side of my abdomen (just under rib cage). lipoma? fat deposit?

Surely: Surely you know we can't answer your question without an examination. What you describe as a fatty lump may be something else entirely. Please see your GP for a definitive answer.

Lipoma: It may well be a lipoma which is a benign fatty tissue growth that is moveable and easily palpated under the skin. They can be left alone unless they're in a place where they will be continually irritated. A physician would have to examine you to confirm the diagnosis.

Safe to observe: While the other doctor is right-an absolute diagnosis cannot be made without an exam, this is most likely a lipoma. I think it is safe to observe IF it is not growing or not painful