"narrow, strict" (late 13c.), from Old French estreit, estrait "tight, close-fitting, constricted, narrow" (Modern French étroit), from Latin strictus, past participle of stringere (2) "bind or draw tight" (see strain (v.)). More or less confused with unrelated straight (adj.). Related: Straightly.
c. 1200, "fasten (clothing, etc.) with laces and ties," from Old French lacier "entwine, interlace, fasten with laces, lace on; entrap, ensnare," from laz "net, noose, string, cord" (see lace (n.)). From early 14c. as "tighten (a garment) by pulling its laces." From 1590s as "to adorn with lace;" the meaning "to intermix (coffee, etc.) with a dash of liquor" (1670s) originally also was used of sugar, and comes via the notion of "to ornament or trim," as with lace. Meaning "beat, lash, mark with the lash" is from 1590s, from the pattern of streaks. Related: Laced; lacing. Laced mutton was "an old word for a whore" [Johnson].
"conventional," especially "heterosexual," 1941, a secondary sense evolved from straight (adj.1), probably suggested by straight and narrow path "course of conventional morality and law-abiding behavior," which is based on a misreading of Matthew vii.14 (where the gate is actually strait), and the other influence seems to be from strait-laced.
<a href="https://www.etymonline.com/word/strait-laced">Etymology of strait-laced by etymonline</a>
Harper, D. (n.d.). Etymology of strait-laced. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/strait-laced