A drop or two of penetrating oil might help. But at this point I might instead hold a piece of wood against the handle and give that a sharp whack with the shaft of a large screwdriver. That might break it loose.

I had the same problem last week. After struggling for a while I got out a pair of pry bars and slipped the short parts of the "L's" under the handle opposite one another. Then I pried slowly, but firmly, on both pry bars until the handle popped off. Obviously you may need to be careful about what you are prying against, but this worked for me with no damage. The handle was just a tight fit on the shaft it surrounded, and years of water, soap, and corrosion had "glued" the two parts together pretty well. After I finished my repair, the parts went back together easily without my having to clean up anything first.