  Vortex lattice patterns with transitions from regular to other variety vortex
shapes are predicted in rotating binary mixtures of dipolar Bose-Einstein
condensates loaded in squared optical lattice. We focus our investigation in
the experimentally accessible dipolar isotopes of dysprosium ($^{162,164}$Dy),
erbium ($^{168}$Er), chromium ($^{52}$Cr), and rubidium ($^{87}$Rb), by
considering the binary mixtures ($^{164}$Dy-$^{162}$Dy, $^{168}$Er-$^{164}$Dy,
$^{164}$Dy-$^{52}$Cr and $^{164}$Dy-$^{87}$Rb), which are confined in strong
pancake-shaped trap and loaded in squared two-dimensional optical lattices,
where we vary the polarization angle of dipoles, the inter-species contact
interactions and the rotation frequency. The ratio between inter- to
intra-species contact interaction is used for altering the miscibility
properties; with the polarization of the dipolar species used for tuning to
repulsive or attractive the dipole-dipole interactions. For enough higher
rotation, of particular interest is the regime when the inter- to intra-species
scattering length is larger than one, in which a richer variety of
vortex-lattice patterns are predicted, including vortex sheets and
two-dimensional rotating droplet formations. The patterns can be controlled by
changing the optical lattice parameters, as shown for the symmetric
$^{164}$Dy-$^{162}$Dy dipolar mixture. For mixtures with stronger differences
in the dipole moments, as $^{164}$Dy-$^{52}$Cr and $^{164}$Dy-$^{87}$Rb, only
half quantum vortices and circular ones have been observed, which will depend
on the dipole orientations.
