Leave factory under coating alone or replace it ?

My 68 Valiant is originally a California car with factory undercoating even in the engine bay, I want to strip it from the engine bay and paint it. But not sure about the underneath, If I was to strip it I would reundercoat it with Lizard skin or something so would be it be be best to strip it and see what's underneath the factory undercoating ? or should it be fine since the upper side is mint ? or redo it and leave it cause the factory is doing its job ?