stay over vs lodge

stay over is not a noun while lodge is a noun.

Word	Noun	Adjective	Verb	Adverb
stay over	No	No	Yes	No
lodge	Yes	No	Yes	No

As verbs, lodge is a hypernym of stay over; that is, lodge is a word with a broader meaning than stay over:

stay over (noun)	lodge (noun)
	any of various Native American dwellings
	a hotel providing overnight lodging for travelers
	a small (rustic) house used as a temporary shelter
	small house at the entrance to the grounds of a country mansion; usually occupied by a gatekeeper or gardener
	a formal association of people with similar interests