I know it takes LG & Verizon to forever upgrade to the next Android OS, like with Kitkat it happened May 2014, but with Lollipop they should be faster...the 90 day window has passed since Lollipop has been released
It's on the list to receive Android 5.0, but it's probably a few months away still. My question is, why do you want it? How's your phone running? Normally, an update like this breaks older phones. With the G4 around the corner, the G2 is an older phone and 5.0 might make it run slower, or cause things to act up for no reason. Also, you most definitely will need to perform an FDR, so once again, why do you want it updated?
LG G2 has the same hardware (like CPU, RAM, and HDD) like the Nexus 5...so it wouldn't be an old phone. The phone's running fine on 4.4.2 but an upgrade to 5.0.x wouldn't hurt it because it can take it.