The Paleozoic peak in coal deposition was not due to white rot fungi evolution lagging behind lignin evolution. In fact we have plenty of evidence that fungi were pretty much always able to decompose lignin
> Here, we demonstrate that lignin was of secondary importance in many floras and that shifts in lignin abundance had no obvious impact on coal formation. Evidence for lignin degradation—including fungal—was ubiquitous, and absence of lignin decay would have profoundly disrupted the carbon cycle. Instead, coal accumulation patterns implicate a unique combination of climate and tectonics during Pangea formation.
https://www.pnas.org/doi/10.1073/pnas.1517943113
> Here, we demonstrate that lignin was of secondary importance in many floras and that shifts in lignin abundance had no obvious impact on coal formation. Evidence for lignin degradation—including fungal—was ubiquitous, and absence of lignin decay would have profoundly disrupted the carbon cycle. Instead, coal accumulation patterns implicate a unique combination of climate and tectonics during Pangea formation.