  We describe solutions of 10-dimensional supergravity comprising null
deformations of $AdS_5\times S^5$ with a scalar field, which have $z=2$
Lifshitz symmetries. The bulk Lifshitz geometry in 3+1-dimensions arises by
dimensional reduction of these solutions. The dual field theory in this case is
a deformation of the N=4 super Yang-Mills theory. We discuss the holographic
2-point function of operators dual to bulk scalars. We further describe
time-dependent (cosmological) solutions which have anisotropic Lifshitz scaling
symmetries. We also discuss deformations of $AdS\times X$ in 11-dimensional
supergravity, which are somewhat similar to the solutions above. In some cases
here, we expect the field theory duals to be deformations of the Chern-Simons
theories on M2-branes stacked at singularities.
