It's posibly to start GTAIII on LG GT540, but it will crash all the time and be too much laggy... That's because of too slow processor (600Mhz)... You need another phone for this...
But if you want to see for yourself, I think this will work... Start GTAIII and when it shows a black screen press home button to minimize game... Than start it again from taskbar or try hold home button and start it from there...