Great question! It sometimes takes a non native English speaker to notice these things. Semantics and etymology fascinate me.
Remember, too, that the Martell's home is called The Blue Pine Lodge, and the hotel exterior used for the Great Northern is called the Salish Lodge and Spa, under tribal ownership.
I take a lodge, in the context of Twin Peaks, to be a structure people (or spirits, as it were) live in.
A "lodge" can also refer to a club or organization, a synechdoche or metonymy for the building they hold their meetings in. For instance, the Masons or the Moose Lodge. An "order" of men.
here is the etymology dictionary entry:
lodge (n.) Look up lodge at Dictionary.com 1231, from O.Fr. loge "arbor, covered walk" (Mod.Fr. "hut, cabin, lodge box at a theater"), from Frank. *laubja "shelter" (cognate with O.H.G. louba "porch, gallery," Ger. Laube "bower, arbor"), likely originally "shelter of foliage," from the root of leaf. "Hunter's cabin" sense is first recorded 1465. Sense of "local branch of a society" is first recorded 1686, from 14c. logge "workshop of masons." The verb is c.1225, "to stay in a lodge, to put someone up in a lodge," from O.Fr. logier, from loge. Sense of "to get a thing in the intended place, to make something stick" is from 1611.