Not cutting it. Trees like to be irrigated irregularly and very, very deeply (far more deeply than you would ever irrigate a lawn) as well. Most of the water you pour on the lawn is lost to the trees.

3.5" per day sounds terribly high but I have no direct experience. I'd guess that watering it once a week would be more than sufficient, with drip irrigation being optimal.

I will say that the seeding process, which throws water over my Cleveland pear tree, has increased its health to the point that its grown 6" in a month and is putting out sporadic blossoms four months out of season. That's about a quarter inch of water a day, but the tree is only two years old.

Your oak trees have nothing to do with the problems your having, except for the thinning, which is normal. I have a Live Oak thats at least 4' diameter and I have St.Augustine Turf growing 10' away from the trunk and beyond. I water 3/4" once or twice a week at most in the heat of summer. The grass growing under the oak could go longer than 1 week, but the grass growing in full sun wilts first.

Native, Mature oaks usually do not require irrigation, as they are well adapted to dry conditions. Healthy oaks are even able to survive excessively dry conditions. Those trees have probably been there long before your house was built.

Mature Oak trees have an extensive lateral root system that spreads horizontally out from the trunk to and well beyond the drip line, sometimes as much as 90 feet. With that, 50 gallons of water over that amount of area is not that much. Plus, most of the root system occurs within the top three feet of soil. Your grass roots probably don't extend past 12 inches. Sure your trees are stealing some water and nutrients, but not enough to starve your lawn.

As for watering your lawn: All you have to do is wait till 30 to 50% of the lawn shows signs of stress (wilting) then water with 3/4 to 1" of water. It may take up to 6 weeks to condition your turf to survive several days or more without wilting between irrigations or rainfall. During this time the root system is developing and growing deeper into the soil.

What Type of Soil do you have?

Isn't KBG suppose to be dormant and brown this time of year?

Can you post a Pic?

Thank you for your responses.

"Mature Oak trees have an extensive lateral root system that spreads horizontally out from the trunk to and well beyond..."

Yes, the sewage backed up in my basement last fall was evidence of those lateral-growing roots.

Will get a pic shortly.