Revelation 20:13-15
13 And the sea gave up the dead which were in it, and death and Hades gave up the dead which were in them; and they were judged, every one of them according to their deeds. 14 And death and Hades were thrown into the lake of fire. This is the second death, the lake of fire. 15 And if anyone's name was not found written in the book of life, he was thrown into the lake of fire. NAS
Maybe the better question should be is will the lake of fire burn for eternity since those who are judged will be "thrown into the lake of fire".