  In this paper, we investigate the thermodynamics of Lifshitz black branes in
the presence of a nonlinear massless electromagnetic field. We begin by
introducing the appropriate action in grand-canonical and canonical ensembles
for nonlinear electromagnetic field. The condition on the parameters of the
metric for having black brane solutions will be presented. Since the field
equations cannot be solved for an arbitrary value of the critical exponent $z$,
we obtain a conserved quantity along the $r$ coordinate that enables us to
relate the parameters of the metric at the horizon and at infinity. Then, we
calculate the energy density of the Lifshitz black brane through the use of the
counterterm method generalized for the asymptotic Lifshitz spacetimes. Finally,
we present a relation between the energy density and the thermodynamical
quantities, electric potential, charge density, temperature and entropy
density. This relation is the generalization of Smarr formula for anti-de
Sitter black branes.
