Ok I took a couple more pictures of the ends. The large end has no hole where a pump or something would go in - it just seems to be a large chamber. The small end is hollow and it's threaded like something else would have put on the end. The middle of it looks like you would screw that off, pour whatever into the chamber, then screw it back. I dunno.
If there is no hole or mounting spot on the big tube, and the threaded shaft is hollow, I'll go along with the grease gun guess. Can you move the shaft or disassemble the tube?