I’m with pressman on this... if you can come up with a large enough pot in which to boil the whole thing (in plain water) you will have the best shot at getting out all of the old lube and other accumulated stuff while having the least chance of damaging your press. An added bonus is that most of the lube will float to the to so it can be skimmed off. Be sure to disassemble the press as much as you readily can to give the melted lube a pathway out!
Froggie