You're exactly on the right track. First remove the plug/stopper. Some have a knob that unscrews that reveals a screw that goes into the drain, others have a little set screw under the lip of the plug that is a pain to get to, but needs to be done. After you have removed the plug/stopper, use a 'castle' wrench to remove the drain. It actually threads through the liner, through the tub, through a gasket and into the drain shoe below. Now you can carefully pull up on the liner (I say carefully because this is the thinnest part of the liner). A strong metal coat hanger bent in an 'L' or 'J' will work well. Also standing in the tub and 'walking' out the water will help. After you have removed as much water as possible, while pulling up on the liner have a helper shoot some silicone caulking under the liner. Replace the drain and stopper using fresh plumber's putty (about $1.50 for a little container) and make sure it tightens fully. Fill the tub with straight hot water and let it sit overnight.
This process MAY work, but also may not, because often when water has invaded the liner for a long period of time it destroys the tape that holds the bottom of the liner to the tub. Often the liner fails because the tub was previously painted and the tape is now only adhered to the failed paint and can not be repaired without taking the liner out which almost always requires a new liner.
Can you contact the previous owner? Often the liner has a lifetime warranty that is transferrable. Worth a phone call.
Good luck and feel free to ask more Qs if needed.
Brett
