Are the LPJ's part of the "faded" series? If so, pay attention to how the frets are dressed, how the back of the neck feels, and how the fretboard feels. My Les Paul is a faded series LP. After 2011, the LPJ series too this over as I recall. If I run my hands up/down the sides of the fretbaord, I can feel the frets sticking out. The fingerboard wood is has a very rough finish that turns out to be very rough on my fingers after playing for an hour or so. The back of the neck has a very rough finish too.

Each of these things by themselves isn't too big of a deal, but all together it has caused me to become discontented with the guitar and made me realize you get what you pay for. When I pick up my american standard strat, it feels so smooth and refined in my hands compared to the LP. I wish I had spent the extra $$$ for a regular LP studio. I may sell this guitar and use it to fund a 2014 LP Studio Pro.

Just some things to look for when you are trying the guitar out.