The Hawking radiation considered as a tunneling process, by using a Hamilton-Jacobi prescription, is discussed for both z = 3 and z = 1-Lifshitz black holes. We have found that the tunneling rate (which is not thermal but related to the change of entropy) for the z = 3-Lifshitz black hole (which does not satisfy the Area/4-law) does not yield (give us) the expected tunneling rate: Gamma similar to exp(Delta S), where Delta S is the change of black hole entropy, if we compare with the z = 1-Lifshitz black hole (BTZ black hole, which satisfies the Area/4-law).