  We study the three-dimensional ground state vortex lattice structures of
purely dipolar Bose-Einstein condensate (BEC). By using the mean-field model we
obtain a stability diagram for the vortex states in purely dipolar BECs as a
function of harmonic trap aspect ratio ($\lambda$) and dipole-dipole
interaction strength ($D$) under rotation. Rotating the condensate within the
unstable region leads to collapse, while in the stable region furnishes stable
vortex lattices of dipolar BECs. We analyse stable vortex lattice structures by
solving three-dimensional time dependent Gross-Pitaevskii equation in imaginary
time. Further, the stability of vortex states is examined by evolution in
real-time. We also investigate distribution of vortices in fully anisotropic
trap by increasing eccentricity of the external trapping potential. Breaking up
of the condensate in two parts has been observed with equally shared vortices
on each when the trap is sufficiently weak and the rotation frequency is high.
