chapter (n.)youdaoicibaDictYouDict
c. 1200, "main division of a book," from Old French chapitre (12c.) "chapter (of a book), article (of a treaty), chapter (of a cathedral)," alteration of chapitle, from Late Latin capitulum, diminutive of caput (genitive capitis) "head" (see capitulum). Sense of "local branch" (1815) is from cathedral sense (late 15c.), which seems to trace to convocations of canons at cathedral churches, during which the rules of the order by chapter, or a chapter (capitulum) of Scripture, were read aloud to the assembled. Chapter and verse "in full and thoroughly" (1620s) is a reference to Scripture.
local (n.)youdaoicibaDictYouDict
early 15c., "a medicament applied to a particular part of the body," from local (adj.). Meaning "inhabitant of a particular locality" is from 1825. The meaning "a local train" is from 1879; "local branch of a trade union" is from 1888; "neighborhood pub" is from 1934.
lodge (n.)youdaoicibaDictYouDict
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," from Frankish *laubja "shelter" (cognate with Old High German louba "porch, gallery," German Laube "bower, arbor"), from Proto-Germanic *laubja- "shelter," likely originally "shelter of foliage," or "roof made from bark," from root of leaf (n.).

"Hunter's cabin" sense is first recorded late 14c. Sense of "local branch of a society" is first recorded 1680s, from mid-14c. logge "workshop of masons." Also used of certain American Indian buildings, hence lodge-pole (1805). Feste of Logges (c. 1400) was a Middle English rendition of the Old Testament Jewish Feast of Tabernacles.