C17: from Latin ēlicere to lure forth, from licere to entice
Word Origin and History for elicit
v.
1640s, from Latin elicitus, past participle of elicere "draw forth," from ex- "out" (see ex-) + -licere, comb. form of lacere "to entice, lure, deceive" (related to laqueus "noose, snare;" see lace (n.)). Related: Elicited; eliciting; elicits; elicitation.