Does GTA liberty city work with windows XP service pack 2?

Yes you can if you modify your registry.

Step 1: Run Regedit by Clicking on Start -> Run , type in regedit and press enter

Step 2: Make a backup of your registry (just in case)

Step 3: Browse to "HKEY_LOCAL_MACHINE\SYSTEM\ CurrentControlSet\ Control\ Windows"

Step 4: Modify the value of "CSDVersion" from "0x00000200" (SP2) to the Windows XP SP3 value of "0x00000300"

Step 5: Close registry editor

Step 6: Reboot

Step 7: Start GTA