Well if recovery mode won't let you do a reset I guess you could try the following:
Download a program called fastboot onto your computer (available as a standalone executable for Linux and MacOS, may need to install the SDK on Windows). If you use Windows you may also need to locate a fastboot driver for your phone (I've never done this using Windows, sorry).
Boot the phone into the bootloader (some button combination should get you there).
If it isn't already in fastboot mode (look at the top of the screen) select it from the bootloader menu. If you can't see that but can see a download mode maybe try that (bootloader vary, and I don't know this phone).
With the phone in the right mode, connect it to the computer via USB.
Fastboot is a command line program. So first try the command "fastboot devices" to check it can talk to your phone. It should respond with the phone serial number. If it doesn't then fiddle with cables and bootloader modes until it does (if it can't find fastboot you need to CD to whatever directory you installed it in).
Once fastboot is working try the commands "fastboot erase data" and "fastboot erase cache". I think they will work even with a locked bootloader.
All that a factory reset does is erase those 2 partitions, so those 2 commands are equivalent to a reset. If they complete successfully but it still won't boot the only things left are to try to find out how to reinstall ("reflash") the phone's software or get a new phone. If they don't complete, especially if the data erase fails, this might mean a hardware problem. Either way reflashing with official software (I don't know the tools for LG) is all you have left to try, but it's less likely to to work in the second case (no guarantees anyway).
