lock up vs shut up

lock up is not an adjective while shut up is an adjective.

Word	Noun	Adjective	Verb	Adverb
lock up	No	No	Yes	No
shut up	No	Yes	Yes	No

As verbs, lock up and shut up are synonyms defined as:

lock up and shut up: place in a place where something cannot be removed or someone cannot escape

Other synonyms of lock up include lock, lock away, lock in, put away, shut away.

lock up (adjective)	shut up (adjective)
	closely confined

lock up (verb)	shut up (verb)
place in a place where something cannot be removed or someone cannot escape	cause to be quiet or not talk
secure by locking	refuse to talk or stop talking; fall silent
	place in a place where something cannot be removed or someone cannot escape