  Recent experiments with ultracold lanthanide atoms which are characterized by
a large magnetic moment have revealed the crucial importance of
beyond-mean-field corrections in understanding the dynamics of the gas. We
study how the presence of an external optical lattice modifies the structure of
the corrections. We find that deep in the superfluid regime the equation of
state is well described by introducing an anisotropic effective mass. However,
for a deep lattice we find terms with anomalous density dependence which do not
arise in free space. For a one-dimensional lattice, the relative orientation of
the dipole axis with respect to the lattice plays a crucial role and the
beyond-mean-field corrections can be either enhanced or suppressed.
