Old English lengðu "property of being long or extended in one direction; distance along a line," from Proto-Germanic *langitho, abstract noun from *langaz "long" (root of Old English lang; see long (adj.)) + *-itho, abstract noun suffix (see -th (2)). Cognate with Old Norse lengd, Old Frisian lengethe, Dutch lengte.
Figurative sense of "the distance one goes, extremity to which something is carried" is from 1690s. Phrase at length "to full extent" is attested from c. 1500. As "the length of a swimming pool," 1903. From the notion of "a piece or portion of the extent of anything" come the theater slang sense "a 42-line portion of an actor's part" (1736) and the sporting sense "the length of a horse, car, etc. in a race" used as a unit of measure (1650s).
word-forming element making verbs (such as darken, weaken) from adjectives or nouns, from Old English -nian, from Proto-Germanic *-inojan (also source of Old Norse -na), from PIE adjectival suffix *-no-. Most active in Middle English and early modern English, hence most verbs in -en are comparatively recent.
<a href="https://www.etymonline.com/word/lengthen">Etymology of lengthen by etymonline</a>
Harper, D. (n.d.). Etymology of lengthen. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/lengthen