The second death is dying yet again after the resurrection to judgement. The lake of fire represents the second death.Some things are worse than death.
The second death will consist of eternal punishment without a hope for a reprieve.
Revelation is a bit unique like this. It’ll say something is something else because the idea is it’s representative not necessarily literal. Like this:
Revelation 19
8She was given clothing of fine linen,
bright and pure.”
For the fine linen she wears is the righteous acts of the saints.