The Collaborative International Dictionary of English v.0.48:

Lucidness \Lu"cid*ness\, n.
   The quality of being lucid; lucidity.
   [1913 Webster]

WordNet (r) 3.0 (2006):

lucidness
    n 1: free from obscurity and easy to understand; the
         comprehensibility of clear expression [syn: clarity,
         lucidity, lucidness, pellucidity, clearness,
         limpidity] [ant: abstruseness, obscureness,
         obscurity, reconditeness, unclearness]