  We exploit the Seiberg -- Witten map technique to formulate the theory of
gravity defined on a Lie algebraic noncommutative space time. Detailed
expressions of the Seiberg -- Witten maps for the gauge parameters, gauge
potentials and the field strengths have been worked out. Our results
demonstrate that notwithstanding the introduction of more general
noncommutative structure there is no first order correction, exactly as happens
for a canonical (i.e. constant) noncommutativity.
