The Liriope plants that I grow here in NE Mississippi, zone 8a, have older, lower leaves that look like that in the late fall/winter. I typically will simply run the lawn mower over all the plants in late winter/early spring (before new growth begins), so that the new growth's appearance isn't diminished by that old, tattered, older growth Liriope is also prone to leaf spot, but again, for me at least, this typically is on older growth.
