I recently fought the lower ball joint and the LCA. I was not going to replace the ball joint and I definitely didn't want to destroy it in the process.

So:

Get a puller that can put pressure on the end of the threaded stud. That alone won't get the job done, but it's a start.

Then, carefully heat the outside of the joint for about two minutes with propane.

Then, sharply rap the side of the joint with a hammer a few times.

This one was quite stubborn, but the combination of force from the puller and shock from the hammer, coupled with some heat, got the job done.