You'd probably need a different inverter too, at the very least.
If a laptop had different resolution options, I'd replace the entire top of it (LCD, inverter, plastics, bezel, etc.) for safety and simplicity's sake. I've done it before myself, but it's been a while. (The last time was an IBM Thinkpad T30 that got a 1400x1050 display to replace the 1024x768.)
But most of the newer laptops I've worked on had similar layouts, with all the important monitor bits (not just the LCD) enclosed in the lid.
LVDS is supposedly somewhat standardized - some people go to pretty absurd lengths:
http://forum.thinkpads.com/viewtopic.php?f=28&t=94254
Otherwise, yeah, what ^^those^^ ^^guys^^ said.