Close and shut have the same meaning, but close is more formal than shut. Lock means to close/shut with a key, padlock or bolt.
close (closed, closed)
Close the door, please! All the shops here close on Sundays. shut (shut, shut) Shut the door, please! Did you remember to shut the gate? Don't shut yourself in your room.
lock (locked, locked)
Lock the door, please! Did you remember to lock the gate? Related words and expressions to close down: close permanently. That shop closed down. to shut up: be quiet. Shut up, please! to lock up: shut and lock completely. They locked up the house before going (they locked all the doors and windows). locker (n): place where things are kept and locked at a school, in a club, in a dorm lock (n): what is used to lock something shutter (n): wood or metal cover used for windows or shops