>>Yes, but as with all analogies they fail. The lake of fire discussed at judgement is not the first death but the second which is eternal<<
I agree. If I drop my car into a vat of molten steel, it’s death will be eternal. It ain’t comming back.
Death, by definition, is an ending. And saying it is eternal means it will not be undone.
If I paint a wall blue for all eternity, it doesn’t mean I paint it for all eternity. It means I painted it once and for all eternity it STAYS blue it is (aionios) blueness, but the event that caused it to be blue is finite.
The punishment is death, and it is eternal. It will not be undone.
And
The lake of fire is a physical place. (In contrast annihilation is no place). It burns (a continuous activity) with fire and brimstone, unquenchable (Mark 9:43), with an unending torment for those who enter ("For everyone will be salted with fire" Mark 9:49). This punishment will be experienced eternally and will not be undone.