  We study critical dynamics through time evolution of quantum field theories
driven to a Lifshitz-like fixed point, with $z>1$, under relevant deformations.
The deformations we consider are fast smooth quantum quenches, namely when the
quench scale $\delta t^{-z}$ is large compared to the deformation scale. We
show that in holographic models the response of the system merely depends on
the scaling dimension of the quenched operator as $\delta\lambda\cdot\delta
t^{d-2\Delta+z-1}$, where $\delta\lambda$ is the deformation amplitude. This
scaling behavior is enhanced logarithmically in certain cases. We also study
free Lifshitz scalar theory deformed by mass operator and show that the
universal scaling of the response completely matches with holographic analysis.
We argue that this scaling behavior is universal for any relevant deformation
around Lifshitz-like UV fixed points.
