I have a Kel-Tec .380, which is virtually a clone of the LCP (and less reliable). I added a LaserLyte CK-AMF (which fits both makes) and it is now incredibly accurate at 21ft. I HIGHLY recommend adding a LaserLyte to your LCP for a confidence boost....well at least in low light. It doesn't add much width to the gun and conceals just as easily with the sidemount laser.
Here's may last visit to the range with my Kel-Tec .380 using the LaserLyte at 21ft...rapid fire (7 rounds each).