  A diagonal Bianchi Type III space-time is treated, both at the classical and
quantum level, in the context of Horava - Lifshitz gravity. The system of the
classical equations of motion is reduced to one independent Abel's equation of
the first kind. Closed form solution are presented for various values of the
coupling constants appearing in the action. Due to the method used, solutions
of Euclidean, Lorentzian and neutral signature are attained. The solutions
corresponding to \lamda <> 1 are seen to develop curvature singularities as the
other constants approach their Einsteinian values, in contrast to those with
\lamda = 1 which tend to the known Einstein gravity solutions. At the quantum
level, the resulting Wheeler-DeWitt equation is explicitly solved for \lamda =
1, \sigma = 0 and \lamda = 1/3 . The ensuing wave-functions diverge in the
Einsteinian limit.
