Modern spelling is from c. 1500. The specific sense "hunter's cabin" is first recorded late 14c. Sense of "local branch of a society" is first recorded 1680s, of Freemasons, from an earlier use of lodge as "workshop of a group of masons" (mid-14c.). In the New World the word was used of certain American Indian buildings (1805), hence lodge-pole (1805) and lodge-pole pine (1859).
From late 14c. as "to dwell, live; to have temporary accommodations; to provide (someone) with sleeping quarters; to get lodgings." Sense of "plant, implant, get (a spear, bullet, fist, etc.) in the intended place, to make something stick" is from 1610s. Meaning "deposit" (a complaint, etc.) with an official" is from 1708. Related: Lodged; lodging.
"remove or drive from a resting place," c. 1400, disloggen, from Old French deslogier "to leave or cause to leave a lodging place; expel, drive away," from des- "do the opposite of" (see dis-) + logier "to lodge; find lodging for," from loge "hut, cabin" (see lodge (n.)). Related: Dislodged; dislodging.
"art of moving, quartering, and supplying troops," 1846, from French (l'art) logistique "(art) of quartering troops," which apparently is from logis "lodging" (from Old French logeiz "shelter for an army, encampment," from loge; see lodge (n.)) + Greek-derived suffix -istique (see -istic). The form in French was influenced by logistique, from the Latin source of English logistic. Related: Logistical.
Meaning "large entrance hall in a public building" is from 1590s; in reference to the House of Commons from 1630s. Political sense of "those who seek to influence legislation" is attested by 1790s in American English, in reference to the custom of influence-seekers gathering in the large entrance-halls outside legislative chambers.
If this is correct, the sense development would be from "loft, ceiling" to "sky, air." Buck suggests a further connection with Old High German louft "bark," louba "roof, attic," etc., with development from "bark" to "roof made of bark" to "ceiling," though this did not directly inform the meaning "air, sky" (compare lodge (n.)). But Watkins says this is "probably a separate Germanic root." Meaning "gallery in a church" first attested c. 1500. From 1520s as "apartment over a stable" used for hay storage, etc.