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.