  The Lorentz gas describes an ensemble of noninteracting point particles in an
infinite array of spherical scatterers. In the present paper we consider the
case when the scatterer configuration P is a fixed union of (translated)
lattices in R^d, and prove that in the limit of low scatterer density, the
particle dynamics converges to a random flight process. In the special case
when the lattices in P are pairwise incommensurable, this settles a conjecture
from [20]. The proof is carried out by applying a framework developed in recent
work by Marklof and Str\"ombergsson [21], and central parts of our proof are
the construction of an admissible marking of the point set P, and the
verification of the uniform spherical equidistribution condition required in
[21]. Regarding the random flight process obtained in the low density limit of
the Lorentz gas, we prove that it can be reconstructed from the corresponding
limiting flight processes arising from the individual commensurability classes
of lattices in P. We furthermore prove that the free path lengths of the limit
flight process have a distribution with a power law tail, whose exponent
depends on the number of commensurability classes in P.
