I do not irrigate and I have a mutt lawn but I have been overseeding with TTTF. I do not irrigate. I haven't done as much with the lawn as I should have... at least Milorganite at bag rate at Memorial Day, July 4, and Labor Day.
I can tell when things are starting to dry when my yard gets more of a steely-blue tinge...
This year though my first sign was inconsistent color in the front. The established grass (in the center of the yard) gets lighter while the areas where my Marvel TTTF has been able to really take hold (seems to be anywhere the more established grass isn't) stays a dark green.
This is Saturday:
Here are some historical photos for comparison...
This was August 12, 2018. My Marvel TTTF is the dark stuff. You can see the neighbors around me and how poorly their lawns are faring.
September 11, 2017, just a little over a year after I moved in.
The back yard looks especially beat up after the summer, but I also have two dogs. I know in the fall I'm always discouraged because the yard looks like garbage but for the past two years it's really blown me away how much comes back, even where I thought it was just going to be bare dirt. I overseed in the fall in the front usually, but I haven't overseeded the back for a couple of years and it always comes back strong in the spring. This is definitely the best spring my yards have had since I moved here in 2016, and the latest they've stayed green and lush.