  We prove that the z=1 and z=3 Lifshitz black hole solutions of New Massive
Gravity in three dimensions are the only static axisymmetric solutions that can
be cast in a Kerr-Schild form with a seed metric given by the Lifshitz
spacetime. Correspondingly, we study the issue of uniqueness of Lifshitz
solitons when considering an ansatz involving a single metric function. We show
this problem can be mapped to the previous one and that the z=1 and z=1/3
Lifshitz soliton solutions are the only ones within this class. Finally, our
approach suggests for the first time an explanation as to what is special about
those particular values of the dynamical critical exponent z at finite
temperature.
