  Here we study properties of a homogeneous dipolar Bose-Einstein condensate in
a weak anisotropic random potential with Lorentzian correlation at zero
temperature. To this end we solve perturbatively the Gross-Pitaevskii equation
to second order in the random potential strength and obtain analytic results
for the disorder ensemble averages of both the condensate and the superfluid
depletion, the equation of state, and the sound velocity. For a pure contact
interaction and a vanishing correlation length, we reproduce the seminal
results of Huang and Meng, which were originally derived within a Bogoliubov
theory around a disorder-averaged background field. For dipolar interaction and
isotropic Lorentzian-correlated disorder, we obtain results which are
qualitatively similar to the case of an isotropic Gaussian-correlated disorder.
In the case of an anisotropic disorder, the physical observables show
characteristic anisotropies which arise from the formation of fragmented
dipolar condensates in the local minima of the disorder potential.
