I have a LP Custom, and my binding is 7-ply (w/b/w/b/w/b/W) the capital W is thick-white. You'll need to buy the individual 2-layer binding (w/b x 3 and W, or w/b x 2 and w/b/W), then laminate all the strips together. It is easiest to do it at the same time you're gluing it into the binding channel, so that it will bend easily around the curves. Just make sure you get the glue both into the channel and in between the layers. Hold it firm to the body with filament tape.
On the LP the nitro lacquer is also sprayed over the binding, so to make it look right you'll need to do some spraying and buffing. Given this, it is probably more straightforward to replace the entire binding.