iSync is for syncing Contacts and Calendars only to supported mobile phones and PDAs, of which LG phones are not.
Protected iTunes music will only play on an iTunes equipped Mac or PC, ROKR phone, iPhone or iPod.
iTunes Plus tracks (the ones without DRM) (or music you've ripped yourself) will playback on devices that support the AAC music format, such as recent Sony Ericsson and Nokia handsets.
So, if your LG phone can play AAC format music (which according to the specs it can't, just MP3 and WMA), and it has the ability to transfer files in this format to the phone, then you may be partially in luck.
But as far as syncing directly from iTunes goes, the answer is No.