I had an LCP and liked it a lot. The (heavy) trigger didn't bother me all that much but like GB said, the Custom model of that gun is just about perfect.
I gave that pistol to a widder woman friend of ours when she was over visiting one evening. She is a real estate agent and the conversation got around to self protection since she meets strangers in isolated locations. She used to shoot a lot with her husband and me before he died so after a basic familiarization I wasn't worried about her ability to handle it safely.
I replaced the LCP with a Bodyguard. It's a fine, accurate weapon, hi-ebber, and day is always a hi-ebber, it suffers from an occasional light primer strike. Hi-ebber again, the Bodyguard is a true double action which allows me to cycle the hammer with a second pull of the trigger; a feature the LCP does not have. A second pull of the trigger has never failed to ignite the primer. This light strike fault is well known and appears in many reviews of the Bodyguard.
Normally for me, this flaw would exclude the weapon from daily carry. But the FTF's have grown less and less frequent with use and I find the little gun is in my pocket whenever I leave the house.
All that said, if I were to do it all over again I'd get an LCP Custom or even another LCP. BTW, the LCP is the best deal going since you can get one for around $175 +/- from PSA. I would not get an LCP II as I can't make myself trust striker fired pistols. I know this an irrational prejudice, but it's just the way I feel.