The owners manual with my LCP states very clearly, and in bold red print,
DO NOT USE +P AMMUNITION
That good enough for me. Might not hurt for a few rounds, but why take the chance. For one thing, I shoot way more than a few rounds of my carry ammo through anything I will carry to insure it functions reliably. If you want 9MM performance, get a 9MM. Even 380+P isn't going to equal a 9MM.
For one thing, there is no such thing as +P 380. The only SAAMI +P standards are for 9MM, 38 Spcl., and 45 ACP. Anything advertised as 380 +P is either over loaded higher than standard pressure, or advertising BS.
Mine shoots Hornady Critical Defense without a glitch, and is perfectly accurate.
I feel it has enough power for personal defense.