The Free On-line Dictionary of Computing (30 December 2018):

complete lattice

   A lattice is a partial ordering of a set under a relation
   where all finite subsets have a least upper bound and a
   greatest lower bound.  A complete lattice also has these for
   infinite subsets.  Every finite lattice is complete.  Some
   authors drop the requirement for greatest lower bounds.

   (1994-12-02)