Under watering in fall

My backyard has a number of old-growth oaks in the lawn area. During the peak of summer, my Rachio seemed to be delivering enough water to keep the lawn somewhat healthy. Since the beginning of September, however, I’ve had to do “quick runs” every second or third day - and even then, my grass is stressed (St Louis, MO is experiencing drought conditions). While the zone reports 81% moisture (from my recent manual run), the topsoil is pretty dry.

While I know that mixed vegetation in zones is not ideal, wondering if there is anything I could do to maintain the required irrigation on the grass.

Not sure how to attach pictures of my lawn/settings.