lodge vs stay over

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

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

As verbs, stay over is a hyponym of lodge; that is, stay over is a word with a more specific, narrower meaning than lodge:

Other hyponyms of lodge include sleep over.

lodge (noun)	stay over (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