admit vs lack

admit

verb
  • To be capable of; to permit. In this sense, "of" may be used after the verb, or may be omitted. 

  • To allow to enter; to grant entrance (to), whether into a place, into the mind, or into consideration 

  • To give warrant or allowance, to grant opportunity or permission (+ of). 

  • To allow (someone) to enter a profession or to enjoy a privilege; to recognize as qualified for a franchise. 

  • To concede as true; to acknowledge or assent to, as an allegation which it is impossible to deny (+ to). 

  • To allow to enter a hospital or similar facility for treatment. 

lack

verb
  • To be without, not to have, to need, to require. 

  • To be short (of or for something). 

noun
  • A deficiency or need (of something desirable or necessary); an absence, want. 

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