Servers for the PS3 and Vita titles were permanently shut down.
Sony permanently closed the servers for the PS4 version of LittleBigPlanet 3 , the last remaining official online hub for the series. Little Big Planet PSN
If you are looking to play today, here is the current situation on PSN and beyond: Servers for the PS3 and Vita titles were
In a final move, LittleBigPlanet 3 and its massive library of DLC were permanently removed from the PlayStation Store . Current Availability & Status Little Big Planet PSN