Not sure if it will help or not, if you need the model number or other information, this is a command line (terminal window) that will show your LCD model number and your color profile:
ioreg -lw0 | grep IODisplayEDID | sed "/[^<]*</s///" | xxd -p -r | strings -6
(this makes it easier to find information about replacement parts and if both computers work you should be able to find detailed info about both screens or see if this other screen has your current model # . If the model info is different you should be able to use google for additional info)
I actually did the exact display swap but in the reverse order (I bought a used A1212 display to replace my A1229 display) and everything worked except the isight connector was different, and I was unable to hook it up. But other than that the display worked fine and you should be able to swap it with no problem (as long as you don't mind not having an operational isight cam). In my case I got a flawless display for 100 bux, and that was wayyy cheaper than having it replaced for me with a working isight cam. I never used the cam anyway.