You purchased the house last year so there is, I'm supposing, no information on what the lawn in that area did last year at this time....maybe the same thing you are experiencing. It could be the ground is hard in the area and doesn't accept moisture down to a level that the lawn uses it to its advantage. In other words, maybe the lawn isn't getting water in that area and pays the price. Too much, is as bad as too little. Too much and too little causes short roots which, when the summer heat hits it, dries it up fast. You didn't say whether you fertilize regularly. Turf grass is, like any other plant, needs food. A regular schedule of fertilizing keeps a lawn in good health and even if grubs invade, a turf that is in the best of health can fight it off. I suggest you do an over layering of compost/triple mix or good topsoil...about 1/2" to 1" and do this every spring ....and fall. Then an overseeding at the same times. What this does is builds organic matter into the soil, improves the soil to absorb and hold moisture and results in a tough turf that can stand up to the dry periods or the over-wet times. To find out how much soil/compost to buy, simply measure the area you wish to cover...length times width...IN FEET. Multiply that by the depth IN INCHES the soil you wish to put down...and multiply that figure by 3.....and divide by 1000. The result will tell you exactly, in cubic yards, how much soil to buy. Thus, if you were to cover the entire 1000 square feet with 1" of soil....1000 sq ft X 1" = 1000, then multiply that by 3...= 3000 divided by 1000 = 3 cubic yards of soil would cover the area. By overlayering 1" of soil over the lawn every spring and fall will improve the drainage and water containment quality and improve the lawn's ability to grow grass in difficult times. A good combination of seeds for northern areas is" 40% Kentucky Blue, 30% perennial ryegrass and 30% fescue. This combo makes for a tough lawn that stands up to most what nature throws at it.

teeka - Go ahead and spray, you won't harm the bamboo if you're carefull. Don't spray on a windy day, keep the sprayer on a tight stream, and stay low to the grass.

I do see a slight rolling hill in the soil, with the top of it being on the line between your camera and the righthand edge of the shed. That could cause some waterlogging if the rainfall drains off there and the surrounding bits are a low point. I can't tell if it would get swampy, but it's probably a drainage point. As such, it should be mid-range challenging in terms of grass. I have a swale on the side of my property that gets rather moist in spring and fall, and dries out in summer. Due to the shorter roots on the grasses there, they shock more easily than the rest of the lawn. The designated ornamental tree spot has been a constant battle due to the moisture, and I finally just dropped in an old-fashioned lilac. I wouldn't hold my breath on getting the understory of that tree perfect, so I might be inclined to kill off the grass there and mulch the area around the tree. That doesn't look like thatch, it looks like dead grass. Whether the water killed it, or the soil chemistry is off, or there was a disease, I can't tell offhand. I think I'd consider a Logan Labs soil test here just to be sure.

It looks like you have a bermuda lawn. Do not use Roundup, it will kill your lawn. You can spray the entire with a broad leaf week killer. You can get one that attaches to your hose. You may need to spray it a couple of times. That will take care of the weeds that are not grassy weeds. For the grassy weeds it is best to prevent them with pre emergents. They are granular and are applied like fertilizer. If you are in N. TX then you will need to apply that on March 1, June 1 and Sept. 1. If you live in other parts of TX then check with your County extension agency for the proper dates. Keep your grass cut short, 1-1,1/2" . Taller grass will not be as thick. Mow low and mow often. This will help to thicken the grass. Fertilize once the grass start growing well, lightly every 4-6 weeks if you are trying to improve your lawn. Good luck!