Wait for El Nino to push another 1-hour monsoon over my house like it did yesterday. I'm a country boy. I haven't watered a lawn since the 2011-2012 drought, which was a pointless endeavor I quickly gave up on. If you spoil your lawn with too much water it just wants more and more.
I don't water the lawn either, but everyone who does, does it in the evening or even after sunset. Which makes sense, since you don't want it to evaporate.
Google says St. Augustine bounces back quickly and spreads aggressively so maybe. You could do a second weed killer application closer to fall to kill off the weeds that will spread in your current bare patches. I have a hate hate relationship with my lawn. From reddit: This is 100% a re-sod scenario, there’s no chance it’ll fill back in before weeds completely take over. Healthy St Aug spreads laterally about a foot per month, so when dead spots are bigger than about 4-6 ft it’s time to resod. Don’t dethatch St Aug unless you’re overseeding with something else or there’s an inch of thatch, it’s extremely stressful for it. Compost top-dressing is a gentler and equally effective way to gradually reduce thatch buildup. Bare dirt is terrible for lawn health, sun and rain will deplete and damage the surface soil of organic matter and create a compacted crust that St Aug roots don’t want to establish in. A thin layer of thatch (~1/4”) acts as mulch to retain water and is GOOD for St Aug recovery. Where you have bare dirt the grass doesn’t want to grow in, add a layer of compost or peat or other organic matter.