  We discuss a class of supersymmetric type II non-relativistic solutions with
exact or asymptotic scale invariance. As already emerged from previous
investigations, we find a clear correspondence between anisotropic
d-dimensional vacua and relativistic solutions in (d + 1)-dimensions. We will
show that supersymmetric four-dimensional Poincare' invariant backgrounds in
type IIB can descend to analogous solutions with anisotropic scaling in t and
(x, y). This result can be applied to scale invariant theories, domain walls
interpolating between four-dimensional Lifshitz vacua and more general
solutions with only asymptotic or approximate scaling behaviour.
