Back up all your stuff. Do a wipe cache partition in recovery mode. Do a factory reset.
Since a factory reset will bring your phone back to how it was when you first got it, you'll have to reinstall all your apps, reconfigure your settings, and retrieve your back ups. Sorry to say that this battery issue with LP has many times been remedied by doing the above steps.
Of course, you can just do the wipe cache partition in recovery and hope for the best. Wiping the cache partition will not/should not mess with anything on your phone, so no back up required. YMMV!
Your choice.