  We explore an effective supergravity action in the presence of a massless
gauge field which contains the Gauss-Bonnet term as well as a dilaton field. We
construct a new class of black brane solutions of this theory with the Lifshitz
asymptotic by fixing the parameters of the model such that the asymptotic
Lifshitz behavior can be supported. Then we construct the well-defined finite
action through the use of the counterterm method. We also obtain two
independent constants along the radial coordinate by combining the equations of
motion. Calculations of these two constants at infinity through the use of the
large-$r$ behavior of the metric functions show that our solution respects the
no-hair theorem. Furthermore, we combine these two constants in order to get a
constant $C$ which is proportional to the energy of the black brane. We
calculate this constant at the horizon in terms of the temperature and entropy,
and at large-$r$ in terms of the geometrical mass. By calculating the value of
the energy density through the use of the counterterm method, we obtain the
relation between the energy density, the temperature, and the entropy. This
relation is the generalization of the well-known Smarr formula for AdS black
holes. Finally, we study the thermal stability of our black brane solution and
show that it is stable under thermal perturbations.
