  Several classes of gravitational backgrounds in $3+1$ dimensions have been
proposed as holographic duals to Lifshitz-like theories describing critical
phenomena in $2+1$ dimensions with critical exponent $z\geq 1$. We numerically
explore one such model, characterized by a temperature $T$ and chemical
potential $\mu$, and find how to embed these solutions into AdS for a range of
values of $z$. We find no phase transition going from the $T\ll\mu$ to the
$T\gg \mu$ regimes, and find that the solutions smoothly interpolate between
the Lifshitz-like behavior and the relativistic AdS-like behavior. Finally, we
exploit some conserved quantities to find a relationship between the energy
density $\mc E$, entropy density $s$, and number density $n$, $\mc
E=\frac{2}{3} \left(Ts+\mu n\right)$. We show that this result is expected from
general scaling arguments, and generalizes to $\mc E= \frac{d}{d+1}\left(Ts+\mu
n\right)$ for a theory dual to AdS$_{d+2}$ (Poincar\'e patch) asymptotics with
a local $U(1)$ gauge invariance.
