I have a few words to say about this theory
1. The trees can't 'suck up' all the energy left because energy can't be created or destroyed. The trees would use it, the fungi would decompose it, and more trees would suck up the same nutrients. It's doubtful that the planet would be as fertile ever again because Lavos and his spawn got most of it, but there's probably enough left to keep a continuous cycle going, though rather small
2. Since we're talking about energy usage and trees being the main living thing to survive, can we asume that Lavos will keep all of the energy he ate up inside of him forever? I mean a giant tick-like parasite has to take a dump sometime, doesn't he? Obviously a lot of the energy would be lost forever to the spawn to go to different worlds, but unless Lavos plans on shooting himself back into space to dump his load on another planet, the planet would eventually get all the nutrients back for at least fertile plant growth. I'm guessing that by 2300 he's nearing the end of his life cycle, so he would at least leave a corpse. He probably spent a lot of his stored energy making his babies, so he most likely doesn't have enough energy to go back into space so as not to leave a corpse on the planet. It's entirely possible that'd he'd do it, but it doesn't seem like the logical path.