  We study the anisotropic Ginzburg-Landau and Lawrence-Doniach models
describing a layered superfluid ultracold Fermi gas in optical lattices. We
derive the coefficients of the anisotropic Ginzburg-Landau and the mass tensor
as a function of anisotropy, filling and interaction, showing that near the
unitary limit the effective anisotropy of the masses is significantly reduced.
The anisotropy parameter is shown to vary in realistic setups in a wide range
of values. We also derive the Lawrence-Doniach model - often used to describe
the 2D-3D dimensional crossover in layered superconductors - for a layered
ultracold Fermi gas, obtaining a relation between the interlayer Josephson
couplings and the Ginzburg-Landau masses. Comparing to the Ginzburg-Landau
description, we find that the region of validity of the Lawrence-Doniach model
is near the unitary limit.
