LA is just short for LAHC

See the paper:
http://www.cs.stir.ac.uk/research/publications/techreps/pdf/TR192.pdf
and the powerpoint:
http://www.cs.nott.ac.uk/~yxb/LAHC/LAHC_new.pdf

Originally I believed that this is just another AspirationType than TS applied on LA. But some interesting revelations:

• AspirationType.BETTER_THAN_LAST_STEP_SCORE on TabuSearch would turn it into Hill Climibing
• AspirationType.BETTER_THAN_BEST_SCORE on LateAcceptance is pointless (= same behavior as NONE) because the late score <= bestScore
  As a result, this isn't aspiration at all. TS has aspirationEnabled, but LA has hillClimbingEnabled (see that paper for more info).