We study the time evolution of holographic mutual and tripartite information for a zero temperature $CFT$, derives to a non-relativistic thermal Lifshitz field theory by a quantum quench. We observe that the symmetry breaking does not play any role in the phase space, phase of parameters of sub-systems, and the length of disentangling transition. Nevertheless, mutual and tripartite information indeed depend on the rate of symmetry breaking. We also find that for large enough values of $delta t$ the quantity $t_{eq}delta t^{-1}$, where $delta t$ and $t_{eq}$ are injection time and equilibration time respectively, behaves universally, $i.e.$ its value is independent of length of separation between sub-systems. We also show that tripartite information is always non-positive during the process indicates that mutual information is monogamous.
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