engage vs lure

engage

verb
  • To attract, to please; (archaic) to fascinate or win over (someone). 

  • To enter into conflict with (an enemy). 

  • To come into gear with. 

  • To enter into (an activity), to participate (construed with in). 

  • To draw into conversation. 

  • To mesh or interlock (of machinery, especially a clutch). 

  • To guarantee or promise (to do something). 

  • To engross or hold the attention of; to keep busy or occupied. 

  • To arrange to employ or use (a worker, a space, etc.). 

  • To bind through legal or moral obligation (to do something, especially to marry) (usually in passive). 

  • To enter into battle. 

lure

verb
  • To attract by temptation, appeal, or guile. 

  • To recall a hawk with a lure. 

  • To attract fish with a lure. 

noun
  • Something that tempts or attracts, especially one with a promise of reward or pleasure. 

  • A bunch of feathers attached to a line, used in falconry to recall the hawk. 

  • An artificial bait attached to a fishing line to attract fish. 

  • A velvet smoothing brush. 

How often have the words engage and lure occurred in a corpus of books? (source: Google Ngram Viewer )