  Via the AdS/CFT correspondence, ground states of field theories at finite
charge density are mapped to extremal black brane solutions. Studies of simple
gravity + matter systems in this context have uncovered wide new classes of
extremal geometries. The Lifshitz metrics characterising field theories with
non-trivial dynamical critical exponent $z \neq 1$ emerge as one common
endpoint in doped holographic toy models. However, the Lifshitz horizon
exhibits mildly singular behaviour - while curvature invariants are finite,
there are diverging tidal forces. Here we show that in some of the simplest
contexts where Lifshitz metrics emerge, Einstein-Maxwell-dilaton theories,
generic corrections lead to a replacement of the Lifshitz metric, in the deep
infrared, by a re-emergent $AdS_2 \times R^2$ geometry. Thus, at least in these
cases, the Lifshitz scaling characterises the physics over a wide range of
energy scales, but the mild singularity is cured by quantum or stringy effects.
