Undisturbed grasslands accumulate a lot of organic matter in soils, some from leaf litter, but also from root and rhizome material. So the lignin content of the leaves is only part of the story. Relative lignin content in leaves goes up in the late season in part b/c carbohydrates and nitrogen compounds are translocated out to seeds, rhizomes, or both.
I do not understand the y axis on your graphs, although the patterns look reasonable.
(ps I worked on related issues years ago).