You are making sense to me. To be eternally alive is to live forever. To be eternally dead is to be dead forever.
Revelation 20:11-15 YLT
11) And I saw a great white throne, and Him who is sitting upon it, from whose face the earth and the heaven did flee away, and place was not found for them;
12) and I saw the dead, small and great, standing before God, and scrolls were opened, and another scroll was opened, which is that of the life, and the dead were judged out of the things written in the scrolls—according to their works;
13) and the sea did give up those dead in it, and the death and the hades did give up the dead in them, and they were judged, each one according to their works;
14) and the death and the hades were cast to the lake of the fire—this is the second death;
15) and if any one was not found written in the scroll of the life, he was cast to the lake of the fire.
No one alive is being judged in this judgment. They are all dead. Not alive. Not alive then, not alive forever. They are forever dead.
Much love!