I have been in the siding business for 24 yrs, and I wouldn't recommend installing anything over an existing exterior, especially one that is delaminating. The biggest issue with this is that your existing siding might be hiding other issues that have been generated over the yrs, ie: rot below windows due to moisture infiltration. If the LP siding is coming apart, it won't stop just because you can't see it anymore!
In Canada, all coastal regions require a rain screen now, and for good reason. Fiber cement and other composite products are completely unsealed on the back side, so any water(or vapor) that either infiltrates or escapes from the inside will shorten the lifespan of the new product. If you paint the back, you just voided the warranty on the board.
Also, all new home warranty insurers in BC require the use of building paper(felt) for these products unless you have a rainscreen.