Poor analogy, for life without the sun won't be life for very long. Without photosynthesis, plants die, animals die, people die. But perhaps you prove the point. How long will it take the Lake of Fire to extinguish a soul? The elapsed time may be commiserate with the sins commited.
If God keeps it in existence for all eternity then it couldn't, which is shown from Scripture:
Mt 25: 41, 46; Dan 12:22; 2 Thess 1:7-9 etc.