Many very good reasons not to carry a 22lr for a self defense weapon. Here are a few that come to mind.
A) I live in a state that sees it's share of cold weather, so many a folk dress in layers during the cold weather. What are the odds that a 22lr would make it through several heavy layers, and still penetrate the BG.
B) Of the guns I own and shoot, the 22 has the most FTF, FTE, and FTF. I don't want that on my mind when I need my CCW weapon.
I could list several more, but I feel those are the 2 most obvious.
If I read correctly, you carry a LCP, so why even consider the 22.