The Collaborative International Dictionary of English v.0.48:

Lucidity \Lu*cid"i*ty\, n. [Cf. F. lucidit['e]. See Lucid.]
   The quality or state of being lucid.
   [1913 Webster]

WordNet (r) 3.0 (2006):

lucidity
    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]
    2: a lucid state of mind; not confused

Moby Thesaurus II by Grady Ward, 1.0:

136 Moby Thesaurus words for "lucidity":
   Atticism, ESP, admission of light, appropriateness, balance,
   chasteness, chastity, clairsentience, clairvoyance, clarity,
   classicalism, classicism, clear-cutness, clearness, coherence,
   comeliness, comprehensibility, connectedness, consistency,
   contact with reality, correctness, crystal-clearness,
   crystallinity, definition, diaphaneity, diaphanousness, dignity,
   directness, discrimination, distinction, distinctness, ease,
   elegance, elegancy, explicitness, extrasensory perception,
   felicitousness, felicity, filminess, finish, fittingness, flow,
   flowing periods, fluency, foresight, gauziness, glassiness,
   glasslikeness, good taste, gossameriness, grace, gracefulness,
   gracility, healthy mind, insight, intelligibility, intuition,
   lightness, limpidity, lucence, lucency, lucid interval, luminosity,
   luminousness, marbles, mental balance, mental equilibrium,
   mental health, mental hygiene, mental poise, mind, naturalness,
   neatness, nonopacity, normalcy, normality, normalness, pellucidity,
   perspicuity, plain English, plain speech, plain style, plainness,
   polish, premonition, propriety, psychometry, purity, rationality,
   reason, reasonableness, refinement, restraint, right mind,
   sanemindedness, saneness, sanity, second sight, seemliness, senses,
   sheerness, show-through, simplicity, sixth sense, smoothness,
   sober senses, sobriety, sound mind, soundness, soundness of mind,
   straightforwardness, structure, taste, tastefulness, terseness,
   thinness, translucence, translucency, translucidity,
   transmission of light, transparence, transparency, transpicuity,
   transpicuousness, unadorned style, unaffectedness, unambiguousness,
   uncloudedness, understandability, unequivocalness,
   unmistakableness, vitreosity, vitreousness, vitrescence,
   wholesomeness, wit