Running LEGO Island Xtreme Stunts without a Disc is quite simple actually. By default the game keeps all it's data on the game disc. So doing this will make it run without the disc.However you will need the disc to copy data from.
1. On the disc, copy the folders titled 'cd' and 'cdc'. You'll find these in the "LIXS" folder on the disc.
2. Paste these folders in the directory you installed the game to.
3. Create a shortcut to 'Game.exe'. This is the LEGO Island Xtreme Stunts executable.
4. Open the properties of the shortcut and change the target to:
"C:\Program Files\LEGO Interactive\Island Xtreme Stunts\Game.exe" "C:\Program Files\LEGO Interactive\Island Xtreme Stunts\cd\" "C:\Program Files\LEGO Interactive\Island Xtreme Stunts\cdc\"
Of course you will need to adjust this to the location on your computer. But the basic format is <Game exe path> <cd folder path> <cdc folder path>. You'll have to make sure you write ou the full path like above because when I tried a relative path the game just froze.
And that's it. Enjoy.