  We study the structure and stability of vortex lattices in two-component
rotating Bose-Einstein condensates with intrinsic dipole-dipole interactions
(DDIs) and contact interactions. To address experimentally accessible coupled
systems, we consider $^{164}$Dy-$^{162}$Dy and $^{168}$Er-$^{164}$Dy mixtures,
which feature different miscibilities. The corresponding dipole moments are
$\mu_{\mathrm{Dy}}=10\mu_{\mathrm{B}}$ and $\mu_{\mathrm{Er}}=
7\mu_{\mathrm{B}}$, where $\mu_{\mathrm{B}}$ is the Bohr magneton. For
comparison, we also discuss a case where one of the species is non dipolar.
Under a large aspect ratio of the trap, we consider mixtures in the
pancake-shaped format, which are modeled by effective two-dimensional coupled
Gross-Pitaevskii equations, with a fixed polarization of the magnetic dipoles.
Then, the miscibility and vortex-lattice structures are studied, by varying the
coefficients of the contact interactions (assuming the use of the
Feshbach-resonance mechanism) and the rotation frequency. We present phase
diagrams for several types of lattices in the parameter plane of the rotation
frequency and ratio of inter- and intra-species scattering lengths. The vortex
structures are found to be diverse for the more miscible $^{164}$Dy-$^{162}$Dy
mixture, with a variety of shapes, whereas, for the less miscible case of
$^{168}$Er-$^{164}$Dy, the lattice patterns mainly feature circular or square
formats.
