lodging vs lodgement

lodging and lodgement both are nouns.

Word	Noun	Adjective	Verb	Adverb
lodging	Yes	No	No	No
lodgement	Yes	No	No	No

As nouns, lodging and lodgement are synonyms defined as:

lodging and lodgement: the state or quality of being lodged or fixed even temporarily

Other synonyms of lodging include lodgment.

lodging (noun)	lodgement (noun)
the act of lodging	the state or quality of being lodged or fixed even temporarily
structures collectively in which people are housed
the state or quality of being lodged or fixed even temporarily