you know i just realized that you probably would have some trouble putting an edge in a LP for a couple of reasons:
1. the strings sit much higher on a les paul so you couldn't have a recessed edge, and even if it was sitting high up it may cause intonation issues
2. the neck angle on a les paul is completely different than that of a Jem or other strat-type (to use the most available general term) the strats/jems neck leaves the body straight out, where the LP kind of leaves the body at a bit of an angle, back towards you the player if you were holding it to play it.
In summation, there'd need to be some serious modifications done to a rather delicate set neck instrument. Which would in all likely hood render the guitar unplayable. An edge probably isn't the way to go, even though they're quite possibly one of the best trems out there it'd be impractical to do all these things so you could put an edge on your LP. There is an alternative however: there's a drop in replacement available for tune o matic equipped guitars (i plan on getting one for my sheraton, and putting one on an ibanez iceman with a sustainer, that'd be bad ass.) If you wanna try this out or look up some info on it you can go to stetsbar.com that's the site that sells this thing, they aren't cheap but let's face it, it's a better way to go than the edge. You could of course still try putting an edge on but it'd have to be sitting on top of the body, and even then the string angle may not be right, imo, i wouldn't risk it and get the easy no rout drop in replacement.