engage vs lay off

engage

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

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

  • To guarantee or promise (to do something). 

  • 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. 

lay off

verb
  • To stop bothering, teasing, or pestering someone; to leave (someone) alone. 

  • In painting, to apply gentle strokes to smooth a wet coat of paint so as to remove visible roller- or brush-marks, commonly using a dry brush; a similar technique, but using a loaded laying-off brush, may produce a smooth coat of paint when using a roller or the usual brush techniques would leave marks. 

  • To place all or part of a bet with another bookmaker in order to reduce risk. 

  • To plan out (a navigational course) using a chart. 

  • To cease, quit, stop (doing something). 

  • (of an employer) To dismiss (workers) from employment, e.g. at a time of low business volume or through no fault of the worker, often with a severance package. 

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