  We examine the stability of quasi-two-dimensional dipolar Bose-Einstein
condensates in the presence of weak optical lattices of various geometries. We
find that when the condensate possesses a roton-maxon quasiparticle dispersion,
the conditions for stability exhibit a strong dependence both on the lattice
geometry and the polarization tilt. This results in rich structures in the
system's stability diagram akin to spectroscopic signatures. We show how these
structures originate from the mode matching of rotons to the perturbing
lattice. In the case of a one-dimensional lattice, some of the features emerge
only when the polarization axis is tilted into the plane of the condensate. Our
results suggest that the stability diagram may be used as a novel means to
spectroscopically measure rotons in dipolar condensates.
