  We calculate the Casimir-Lifshitz pressure in a system consisting of two
different 1D dielectric lamellar gratings having two different temperatures and
immersed in an environment having a third temperature. The calculation of the
pressure is based on the knowledge of the scattering operators, deduced using
the Fourier Modal Method. The behavior of the pressure is characterized in
detail as a function of the three temperatures of the system as well as the
geometrical parameters of the two gratings. We show that the interplay between
non-equilibrium effects and geometrical periodicity offers a rich scenario for
the manipulation of the force. In particular, we find regimes where the force
can be strongly reduced for large ranges of temperatures. Moreover, a repulsive
pressure can be obtained, whose features can be tuned by controlling the
degrees of freedom of the system. Remarkably, the transition distance between
attraction and repulsion can be decreased with respect to the case of two
slabs, implying an experimental interest for the observation of repulsion.
