There is nothing intrinsically worse with response time between the lcd's used in projectors and those used in monitors. Lag is made noticeable by excess and unnecessary image processing (like scaling and frame interpolation). These features are (or should be) turned off when "game mode" is turned on and, you have fed the projector the native resolution of the panel.
Except that a lot of projectors don't use a single, cheap LCD. Once you add multiple LCDs, DLP, color wheels, digital distortion correction, etc... the processing gets a little more intensive. My UST laser projector has a lag of ~140ms when in the mode for the best color reproduction (which is amazing, BTW). The game mode, where much of this processing is turned off, has a pretty dull and lifeless image. On the other hand, my triple LCOS panel projector doesn't have as much lag, but it's still slower than my plasma display.
There's just more going on in the guts of projectors which needs to be corrected for the screen being used.