  We use the holographic duality to study quantum quenches of a strongly
coupled CFT that drive the theory towards a non-relativistic fixed point with
Lifshitz scaling. We consider the case of a Lifshitz dynamical exponent $z$
close to unity, where the non-relativistic field theory can be understood as a
specific deformation of the corresponding CFT and, hence, the standard
holographic dictionary can be applied. On the gravity side this amounts to
finding a dynamical bulk solution which interpolates between AdS and Lishitz
spacetimes as time evolves. We show that an asymptotically Lifshitz black hole
is always formed in the final state. This indicates that it is impossible to
reach the vacuum state of the Lifshitz theory from the CFT vacuum as a result
of the proposed quenching mechanism. The nonequilibrium dynamics following the
breaking of the relativistic scaling symmetry is also probed using both local
and non-local observables. In particular, we conclude that the equilibration
process happens in a top-down manner, i.e., the symmetry is broken faster for
UV modes.
