  We study propagation of entanglement after a mass quench in free scalar
Lifshitz theories. We show that entanglement entropy goes across three distinct
growth regimes before relaxing to a generalized Gibbs ensemble, namely 'initial
rapid growth', 'main linear growth' and 'tortoise saturation'. We show that
although a wide spectrum of quasi-particles are responsible for entanglement
propagation, as long as the occupation number of the zero mode is not
divergent, the linear main growth regime is dominated by the fastest
quasi-particle propagating on the edges of a widen light-cone. We present
strong evidences in support of effective causality and therefore define an
effective notion of saturation time in these theories. The larger the dynamical
exponent is, the shorter the linear main growth regime becomes. Due to a pile
of tortoise modes which become dominant after saturation of fast modes, exact
saturation time is postponed to infinity.
