lost cause vs crusade

lost cause and crusade both are nouns.

Word	Noun	Adjective	Verb	Adverb
lost cause	Yes	No	No	No
crusade	Yes	No	Yes	No

As nouns, crusade is a hypernym of lost cause; that is, crusade is a word with a broader meaning than lost cause:

lost cause: a defeated cause or a cause for which defeat is inevitable
crusade: a series of actions advancing a principle or tending toward a particular end

Other hypernyms of lost cause include campaign, cause, drive, effort, movement.

lost cause (noun)	crusade (noun)
a defeated cause or a cause for which defeat is inevitable	a series of actions advancing a principle or tending toward a particular end

lost cause (verb)	crusade (verb)
	go on a crusade; fight a holy war
	exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for