It's too hot for you to be watering with frequency and it's been raining (relatively) a lot this year in Texas (though the last few weeks have been less wet). I would suspect fungus, but you should also test for bugs. Take a 5-gallon container. Fill it with water and dump it on the edges of the brown area. If you see a billion harmful bugs come up after 10 minutes or so, you know it's that and that you need to spray Bifen XTS or something else, otherwise try a curative round of azoxy. You can also fertilize and try to get the grass to grow through it but some forms of fungus need to be treated ASAP. FYI June is prime fungus season for Texas due to the temp and the still ongoing rain. Fungus problems generally go away in July and August unless the lawn is frequently irrigated. Water deep, in the morning (not at night if you're night watering), and less frequently (once or twice a week, .5-.75" each time, 1-1.5" total each week accounting for irrigation and rains) in the future. Once your yard recovers (definitely don't do it now), try PGR to strengthen the grass and make it more dense, drought and shade tolerant.

Could be an issue with shade considering the picture has a giant shade area covering the brown area, but I can't be certain without other angles and you didn't say the grass has always struggled just that it recently turned brown. Could be standing water but I don't see blotches of grass clippings or evidence of a flow to really go that route.

Again, my money is on fungus but you should listen to other opinions that may come up from the moderators.

 

That looks like webworm damage to me.