  In this paper, based on the new version of the gedanken experiments proposed
by Sorce and Wald, we examine the weak cosmic censorship in the perturbation
process of accreting matter fields for the charged dilaton-Lifshitz black
holes. In the investigation, we assume that the black hole is perturbed by some
extra matter source satisfied the null energy condition and ultimately settle
down to a static charged dilaton-Lifshitz black hole in the asymptotic future.
Then, after applying the Noether charge method, we derive the first-order and
second-order perturbation inequalities of the perturbation matter fields. As a
result, we find that the nearly extremal charged dilaton-Lifshitz black hole
cannot be destroyed under the second-order approximation of perturbation. This
result implies that the weak cosmic censorship conjecture might be a general
feature of the Einstein gravity, and it is independent of the asymptotic
behaviors of the black holes.
