On a Les Paul neck I would actually suggest tuning it up a couple steps above normal pitch and leave it sit a few days, they are huge thick necks. If that doesn't work then as glen said you will have to have a luthier look at it. Les Paul necks are difficult for a few reasons. First they are very thick, it's tough to force them safely, second, the finish used Gibsons is very soft, it will need to be buffed out afterwards probably, and last, being a set neck is going to make it harder as well.
The cost could be anywhere as low as $50 is all it takes is some pressure and force to bring it back, to a significant amount if the back bow is bad enough. In a worst case scenario the frets would need to be removed and the fretboard re-levelled then refretted. I would figure you'd be looking at around $450 to $550 for that job.
If you tune it up a few steps above pitch, you'll probably need to leave it sit for at least a week by the way, it will take some patience. For what it's worth though, I've never had a neck come through the shop that I couldn't get rid of the back bow by bending it.