Critical strike will increase the physical portion of the damage, if any, but won't affect the lightning damage. For example, with Lightning Fury, you throw a javalin - the critical strike skill will make that javalin do extra damage. It won't affect any of the lightning bolts that come out, though.
Peirce works similarly. You throw the javalin for lightning fury - that javalin carries the lightning charge. It strikes an opponent, sends off lightning, and with Peirce, it has a chance to carry through and strike another person behind the first. If it does so, it sends off more lightning from that person, as well. This continues until it can no longer peirce.