mature trees growing in non-irrigated lawn
Would it be a good idea to mulch mature trees in a circle out to the drip line, preventing grass from growing in that area? It seems to me that whatever rain falls would then go to the tree instead of the grass. Or, maybe just a wide band of mulch spanning the drip line would be enough, with plantings of some sort in closer to the trunk. the trees are huge, mostly oaks.
District of Columbia
It is difficult to grow grass under large mature trees. There is a lot of competition for moisture and nutrients and lack of sunlight. It is a good idea to mulch out to the dripline of the tree.
You can plant some shade perennials, a groundcover, place containers of annuals in the area, or simply mulch. Make sure mulch is no thicker than several inches and keep away from the base of the trunk.