I've heard that the G2 uses Slimport to output video. If that's not the case, then it uses MHL. Either way, you'll need an adapter. I'd look into it and find out for sure which one it is, then do a little more digging to find out what you'll need. Personally I've never used either.
Sent from CAMACHO, my Verizon G2 (VS980) running PAC ROM.
The Aphotic Chaotic
LG G2 VS980 (Verizon) [JB 4.3] PAC-man ROM
Nexus 7 [JB 4.2.2] XenonHD