Are there settings in the setup menus for the PS3 and 360 to compensate for HDTV lag?

May be...

I was having a general conversation with a friend. I was confident that both Microsoft and Sony would include such a seemingly simple solution for their gamers, but I cannot find a source online and am not at home to check the PS3 menu.

No. Your TV is supposed to have such settings, not the consoles themselves.