For a long time now I've been trying to gather thoughts on what the second death, or, lake of fire, means. That it's not a literal lake filled with literal fire is without doubt but it's still something hard to put into words. The following is not the whole of it, but a tiny part.. and food for thought.
A quote from David Sanderson (and I don't know who he is, only what he's reported to have said)..
"What is the second death...?" The second death is Judgment. The scripture has many names for it. It's the work that parental and almighty God intended (and absolutely able) to finish 'creating mankind in His image', 'conforming him to the image of His Son', 'scourging every son that He receives', 'burning out (fire) ...of dross' etc. It's also the 'taking up the cross and following', the, 'dying to self', etc.
It's not always 'punitive' and often altogether lovely. It's educational, spiritual, beneficial, and scriptural.
Judgment fails if it's 'eternal' (never ending), without redemptive or corrective benefit, or unjust by being either insufficient for the task, or demonically cruel as in the pagan/christian 'hell'. God is the perfect Father, and that makes Him the perfect Judge. (perhaps that also answers your question about the unbelieving 'good' man). God doesn't fail.
People who believe both Scripture and the successful creation/salvation of all humankind know that this is no easy, flippant Gospel.