The hair dryer or heat gun will work best. Remove the sizing die, turn it topside down over a container, and heat the bottom. Might use a coat hanger to hold it suspended. This will allow the lube to run our freely. Might also put a slight tilt up on the front as there is a small reservior there under where the die goes that will need to be cleaned. Usually once the lube melts it flows out pretty easy.
Ive cleaned up three of the, 2 Lyman and one older Saeco. They all work about the same. Just don't get them too hot, once the lube starts to drip out, stop heating until it cools and stops, then add a little more heat. My Saeco took the longest at about an hour and a half from start to finish. That lube was ridiculous hard and seemed to take forever to start dripping.