  We search a gravitational system which allows a non-relativistic hybrid
geometry interpolating the Schr\"odinger and Lifshitz spacetimes as a solution,
as a continuation of the previous work employing a flow equation. As such a
candidate an Einstein-Maxwell-Higgs system naturally arises and we verify that
this system indeed supports the hybrid geometry with the help of a gauge-fixing
term for diffeomorphism. As a result, this gravitational system may be
interpreted as a holographic dual of a general non-relativistic system at the
boundary.
