No, game sharing is not possible in Grand Theft Auto: Liberty City Stories.
Game sharing (or account sharing) is a feature native to modern digital platforms like Steam, the Epic Games Store, and Xbox Game Pass. Liberty City Stories was originally released on the PSP and PlayStation 2—platforms that lack the digital licensing infrastructure required for this functionality. The game license is tied to the physical UMD/disc or the specific console's internal memory.
While you cannot share the license digitally, you can still experience the game cooperatively via: