Well, with those old japanese LP's the problem often is that the previous owner(s) didnt always care for them good enough. So i often found them to have bad frets, cr@ppy set neck and sometimes they had corroded pickups and hardware to the point it needed to be replaced.
So checking it out prior to buying would be advicable IMO. If you try it out i would advice to try and listen to the guitar from a recording POV, a custom should sound transparant and dry IMO which is best for recording and post processing IMHO.
The japanese Epi's were made following the gibson tradition, so an old epi LP custom will be one of the heaviest guitars out there, not a bad thing if you are used to a bit of weight, still lengtly practice sessions micht turn out to be quite challenging. On the other hand, if you play sitting down alot those customs do balance best IMHO.
As an alternative for a LP custom model, i allmost bought an epi Genesis, which are early 80's double cutaway LP's. They are dirt cheap but look pretty yawlfull. Still soundwise they are all good and they also made custom versions of those, the custom genesis version i played did cost 250 pounds or thereabout. It also has a standard pickup split switch by the way. In comparison these genesis' dont balance well at all when sitting down.
PS. i would spend 450 pounds on a perfect MIJ LP, but thats about the real limit. If you allready have a LP Standard, i would also suggest to try and find a custom with maple neck, just for above mentioned recording purposes.
EDIT: When talking about the sound of a custom i mean in an acoustic way, i prefer alnico II pafs on such a custom which is a superb match trancparency wise, it will also add to the warmth and sweet melodic tones one would expect from a fine instrument.