Would it cause lag if you play it on a LCD TV
While potential lag is a possible issue, I wouldn't think the type of TV would matter. If the controller itself is causing lag, I would think it would happen no matter what type of TV you are using.
Of course LCD TVs may cause lag themselves if they do not have some type of "game mode," but this should be unrelated to the wireless controller. It would happen no matter what type of controller you are using.
Unless your concern is that you have lag with your LCD TV AND your wireless controller that compounds into a situation that makes your game unplayable.