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The Final Judgement that determines that the wicked are to be cast into the Lake of Fire is detailed in Rev. 20.
5 But the rest of the dead lived not again until the thousand years were finished. This is the first resurrection. [If there is a 1st resurrection there must be at least a second]
It will be 1000 years after the resurrection of the righteous that the wicked will be resurrected for Judgement before being cast into the Lake of Fire.
12 And I saw the dead, small and great, stand before God [This is the only place that makes sense for the second resurrection]; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works. [After being raised the dead are judged]
13 And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works. [Every dead person will be raised at some point]
14 And death and hell were cast into the lake of fire. This is the second death. [The punishment is then executed]
It is very poetical in nature, but these verses together show that the dead are indeed resurrected, just as the righteous, shortly before being judged then cast into the Lake of Fire, the second death. Some do argue that the resurrection is not bodily, however, they are a small minority.
I don't think justice necessitates the resurrection, unless you adhere to Annihilationism. It just happens to be the order that it will be done according to the Bible. I currently have a related question about why the wicked are raised only to suffer eternal hell because it seems unnecessary to me to give the wicked a body unless punishment has something to do with the body.