I have to say, I don't remember any instance of LMGTFY that uses that exact website/term. So I'm having a hard time seeing the problem.
However, I fully agree that the site/the phenomenon are a rude and condescending response in the context of our site. So I would approve of a ban.
When I see people being referred to Google, it's usually in a different form though, like here: Why did dialup modems make noise?