The “second death” is permanent, for there is no atonement sacrifice for those going into it. The apostle Paul wrote:

“If we practice sin willfully after having received the accurate knowledge of the truth, there is no longer any sacrifice for sins left, but there is a certain fearful expectation of judgment and there is a fiery jealousy that is going to consume those in opposition.”​—Heb. 10:26, 27.

The “lake of fire” or “second death,” though always possible for God to use on the willfully disobedient, will not hold any threat to those who have been proved everlastingly loyal through the test of Satan’s loosing after the end of the thousand years of Christ’s reign.