Sounds like you got a worse battery from LG than most of us. Im still not convinced that the issue is software (as LG is saying), it might be able to be HELPED with software (undervolting the CPU and such) but the batteries are just junk, ESPECIALLY with this kind of hardware. So I would recommend getting a higher capacity battery, one from Ebay would do the trick (just grab a prepaid visa card)
Other than that try:
Running Juice Defender (seriously I get 50-100% better battery life with this app, on my old LG Optimus M I used to get almost 48 hours of standby time and at LEAST 24 hours with moderate use/gaming)
Delete Swype. Unless you use Swype, back it up and delete it, it is NOTORIUS for draining battery. If you use it, then search around and sign up for and download the Beta, reports are that it uses less battery than the current version
Set up Maps right. Go into the settings and set the "cache map tiles" to wifi/charging only, that way maps wont keep trying to load tiles in the background when your on the go. Dont leave your GPS antenna on. And use the new "download for offline use" option to download a map of your area so Maps NEVER has to actually download tiles as long as you stay in that area. doing all this put my maps down to using about .5%
Turn off 4G when you dont use it. Use Power Control Plus app (the 2g/3g option is what youll need to use) to turn off the 4G antenna, the 3g uses less and is just fine for most tasks, you can always turn it back on when you need it.
Use a program (I like Rom Toolbox Pro, for $5 it has tools to do everything mentioned here and ALOT more) to to create some CPU profiles. I like one for "screen on" that has your normal max cpu and a minimum of like 600 with the smartassv2 governor, and one for "screen off" with a max of like 600 and a minimum of 432 with a conservative governor. Doing this gave me at least another hour or two of standby.
Use Rom Toolbox (or another program) to keep as many apps from starting as possible, the only things you need when you start is widgets, apps that use push notifications (like email, mms, facebooc, etc) and system apps. NO, that game does not need to start with your phone
and finally, find the lightest apps and consolidate them as much as possible. For instance Rom toolbox let me get rid of about 10-15 apps I had before. Also, Friend Caster not only uses 20-30 less memory, but ALSO has more options.
There you go, hope this helps.