In this note, we are interested on the event of extinction and the property of coming down from infinity of continuous state branching (or CB for short) processes with competition in a Lévy environment. In particular we prove, under the so-called Grey’s condition together with the assumption that the Lévy environment does not drift towards infinity, that for any starting point the process becomes extinct in finite time a.s. Moreover if we replace the condition on the Lévy environment by an integrability condition on the competition mechanism, then the expectation of the extinction time is finite. Finally, if we assume that the competition mechanism is convex and that the jump structure associated to the environment possesses some positive exponential positive moments then we deduce that the process comes down from infinity.