  We use a WKB approximation to establish a relation between the wavefront
velocity in a strongly coupled theory and the local speed of light in a
holographic dual, with our main focus put on systems with Lifshitz scaling with
dynamical exponent z. We then use Einstein equations to relate the behavior of
the local speed of light in the bulk with the null energy condition (NEC) for
bulk matter, and we show that it is violated for Lifshitz backgrounds with z<1.
We study signal propagation in the gravity dual and show that violations of the
NEC are incompatible with causality in the strongly coupled theory, ruling out
as holographic models Lifshitz backgrounds with z<1. We argue that causality
violations in z<1 theories will show up in correlators as superluminal modes
and confirm this for a particular example with z=1/2. Finally, as an
application, we use z<1 solutions to uncover regions of the parameter space of
curvature squared corrections to gravity where the NEC can be violated.
