My apologies - I must have been tired.
Since you're using a LCD panel that only has VGA input, and your laptop (used as an HTPC, I'm guessing) only does VGA output, You'd have to run the XBox independently of the laptop.
After a little searching, I think this might be your best option:
Neoya X2VGA 2 (you might be able to find the earlier X2VGA or X2VGA+ cheaper)
QUOTE
Comparing with the former X2VGA, the X2VGA 2 is compatible with various gaming consoles and video devices, and presents you with the perfect visual performance by its brand-new design of video processing circuits. Moreover, the newly integrated two sets of video inputs and PC pass-through function on the X2VGA 2 even allow a quick switch between your gaming consoles and PC.
I used the following Google search to find this info:
xbox -360 vga projector