  Following arXiv:1005.3291 [hep-th], we discuss certain lightlike deformations
of $AdS_5\times X^5$ in Type IIB string theory sourced by a lightlike dilaton
$\Phi(x^+)$ dual to the N=4 super Yang-Mills theory with a lightlike varying
gauge coupling. We argue that in the case where the $x^+$-direction is
noncompact, these solutions describe anisotropic 3+1-dim Lifshitz-like systems
with a potential in the $x^+$-direction generated by the lightlike dilaton. We
then describe solutions of this sort with a linear dilaton. This enables a
detailed calculation of 2-point correlation functions of operators dual to bulk
scalars and helps illustrate the spatial structure of these theories. Following
this, we discuss a nongeometric string construction involving a
compactification along the $x^+$-direction of this linear dilaton system. We
also point out similar IIB axionic solutions. Similar bulk arguments for
$x^+$-noncompact can be carried out for deformations of $AdS_4\times X^7$ in
M-theory.
