  We study $AdS\times X$ null deformations arising as near horizon limits of
D3-brane analogs of inhomogenous plane waves. Restricting to normalizable
deformations for the $AdS_5$ case, these generically correspond in the dual
field theory to SYM states with lightcone momentum density $T_{++}$ varying
spatially, the homogenous case studied in arXiv:1202.5935 [hep-th]
corresponding to uniform $T_{++}$. All of these preserve some supersymmetry.
Generically these inhomogenous solutions exhibit analogs of horizons in the
interior where a timelike Killing vector becomes null. From the point of view
of $x^+$-dimensional reduction, the circle pinches off on these horizon loci in
the interior. We discuss similar inhomogenous solutions with asymptotically
Lifshitz boundary conditions, as well as aspects of Lifshitz singularities in
string constructions involving $AdS$ null deformations. We also briefly discuss
holographic entanglement entropy for some of these.
