The only reason why you’re experiencing Lag on a projector is that you’re a cheapskate. The “Lag” you’re experiencing is caused by Upscaling on the display device’s image processor.
Why is it upscaling you ask? It’s because you’re using a display output that is lower than the native resolution of the projector. The projector has to spend some time bringing your output closer to a native resolution of the projector or TV. Therefore if you used a 480 native projector for your ps2 games instead of a 1080i native you would experience “lagless” gameplay. Yet if you have a PS3 outputting to 480 on a 1080i projector you will experince “lagged” gameplay and look like a moron blaming your losses on the projector.
So…. Buy some damn Component or HDMI cables you moron.
Nevertheless, for exhibition play, your best solution would be to go with dual display out 1 to a CRT 1 to a projector to support older consoles PS2 and earlier.
Further explanation about Projectors can be found here