  Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties X
in positive characteristic which endow the Poisson bracket on X with the
structure of a restricted Lie algebra. We consider deformation quantization of
line bundles on Lagrangian subvarieties Y of X to modules over such
quantizations. If the ideal sheaf of Y is a restricted Lie subalgebra of the
structure sheaf of X, we show that there is a certain cohomology class which
vanishes if and only if a line bundle on Y admits a quantization.
