1550s, "cloister, covered walk," from Medieval Latin laubia, lobia "covered walk in a monastery," from a Germanic source (compare Old High German louba "hall, roof;" see lodge (n.)).
Meaning "large entrance hall in a public building" is from 1590s; in reference to the House of Commons from 1630s.
lodge(n.)
Middle English logge, mid-13c. in surnames and place names; late 13c. as "small building or hut," from Old French loge "arbor, covered walk; hut, cabin, grandstand at a tournament" (12c.), from Frankish *laubja "shelter" (cognate with Old High German louba "porch, gallery," German Laube "bower, arbor"), from Proto-Germanic *laubja- "shelter." On a widespread guess (backed by Watkins, OED) this likely originally meant "shelter of foliage," or "roof made from bark,"...
