The Collaborative International Dictionary of English v.0.48:

Luckiness \Luck"i*ness\, n.
   1. The state or quality of being lucky; as, the luckiness of
      a man or of an event.
      [1913 Webster]

   2. Good fortune; favorable issue or event. --Locke.
      [1913 Webster]

WordNet (r) 3.0 (2006):

luckiness
    n 1: an auspicious state resulting from favorable outcomes [syn:
         good fortune, luckiness, good luck] [ant: bad luck,
         ill luck, misfortune, tough luck]