For example the famous verse John 3:16, which makes it clear that those without real faith in the Son will perish. So obviously that is death. Will that end? Of course not, it will be everlasting death. No more resurrection for those who perish in the lake of fire.
So we can go for more on this to where the lake of fire is mentioned explicitly, in Rev. 20. For example verse 14 says this is the second death, the lake of fire. It says death. No resurrection after that is mentioned, so it is eternal death.
Or I can mention also for example 2 Thess. 1:9, that they will suffer the punishment of everlasting destruction. If someone is destroyed, he is dead. And this destruction is everlasting, so it never ends, he will never be alive again. And this verse says it is a punishment. So the punishment is everlasting death.
Or I can mention for example 2 Peter 2:12, that these people, like irrational animals, will be destroyed. Now think about it, what is the destruction of those people and animals, is it death or suffering and pain, as you say? Does it look logical that God would punish animals, for example my dog, with eternal suffering? Why would God do anything like that? A loving dog? Just because my dog did not have faith in the Son? It would be bizarre. I don't know of any Christian who believes that the animals will suffer forever, in the lake of fire. So it is everlasting death. And for animals, it is not in the lake of fire, they will not be resurrected, they die and from that time on, it is everlasting death. And similarly for the unworthy humans, though after being thrown in the lake of fire, then the end will be the same, everlasting death. Not everlasting suffering for the animals and unworthy humans, after all it is called destruction. My dog was destroyed when he died. No more heartbeat, no nothing, his life was destroyed. The evil people will be destroyed by being burned up in the lake of fire. They will become ashes, Mal. 4:3. Ashes are dead forever.