It depends on which tuners came on your Studio. Different years had different style tuners. These work on some of them. Actually, if your guitar came factory with keystone tuners or Grover stule tuners, it should still work. They both require a 10mm hole which the LP has. The only thing you may have to do is make a tiny hole for the set screw to go into???? If so, it is a VERY easy task. http://www.stewmac.com/shop/Tuners/Guitar,_solid_peghead_tuners/Grover_Locking_Guitar_Machines.html
Curious, why do you feel you need locking tuners? They wont really help anything out on a LP. If you are having tuning stability issues, the usual culprit in a LP is the nut. No, you dont need a new one in most cases, it just needs to be worked on properly.
