crocodile tears vs lip service

crocodile tears and lip service both are nouns.

Word	Noun	Adjective	Verb	Adverb
crocodile tears	Yes	No	No	No
lip service	Yes	No	No	No

As nouns, lip service is a hypernym of crocodile tears; that is, lip service is a word with a broader meaning than crocodile tears:

crocodile tears: a hypocritical display of sorrow; false or insincere weeping
lip service: an expression of agreement that is not supported by real conviction

Other hypernyms of crocodile tears include hypocrisy.

crocodile tears (noun)	lip service (noun)
a hypocritical display of sorrow; false or insincere weeping	an expression of agreement that is not supported by real conviction