I had the lower ball joint on my 1997 lincoln town car pop out of the control arm. How do I get the rest of the ball joint assembly out of the control arm so I can install the new ball joint?

frist there's a recall on lower ball joints, give the dealer a call to see if yours is covered.

if not covered, you'r going to need a specail tool"large c clamp", to remove the joint, call a few part stores, some rent the tool.
here's the replacement info:

Ball Joint, Lower

REMOVAL

Raise vehicle on hoist.
Remove front wheel spindle.
Remove and discard joint boot seal.

Press out front suspension arm bushing joint using U-Joint Tool T74P-4635-C or equivalent, Ball Joint Remover D89P-3010-A and Receiving Cup D84P-3395-A4 or equivalent.

INSTALLATION

Install front suspension arm bushing joint with Ball Joint Remover D89P-3010-B or equivalent, Receiving Cup D84P-3395-A4 or equivalent and U-Joint Tool T74P-4635C. NOTE: When installing a new front suspension arm bushing joint, the protective cover must be left in place during installation to protect the ball joint seal. It may be necessary to cut off the end of the cover to allow it to pass through the receiving cup.
Discard the protective cover and check the front suspension lower arm ball joint to make sure it is fully seated in the front suspension lower arm and ball joint seal is free of cuts or tears.
Install front wheel spindle.
Check wheel alignment.

as to be pressed out. you can rent the tool for autozone (you get all of your money back when you return the tool).