That lawn will return, but since it's like it is, you have a decision to make. You have far too much soil in the yard. See where it slopes down to meet the concrete...it should be level with the concrete. It would probably be easier to build a brick or concrete retaining wall about 2-3 inches high to hold all the mud in and contain the yard. The alternative is to have the excess soil removed which would take out all the grass, too.

Stop watering for now. On March 1st, if you have not received an inch of rainfall in February, then set your new sprinkler system to water about 1 inch. You'll have to measure that with tuna or cat food cans set around the yard. Time how long it takes to fill the cans and set your sprinkler to water that long every time. Then forget about watering until April 1st. If you have not received at least 1/2-inch of rain in March, then water 1 inch again for April. As the temperature rises into the 70s, water every 3 weeks. With temps in the 80s, water once every 2 weeks. With temps in the 90s water every week. Again, if you have rain, postpone the irrigation. That is all the water the lawn needs, but when you water, do the 1 inch. In Houston I would be surprised if you ever need to water more than once per week.

In mid April, if you have weeds, spot spray them with an atrazine product like this one...

Watch for overspray and don't spray your shrubs. This herbicide takes about 3 weeks to see the full effect. Some plants will shrivel up quickly and others will take the full 3 weeks. But then you'll notice there are no weeds in the lawn. It works very well on the winter rye grass and poa annua and seems to kill the seeds for those plants, too.

In late May, fertilize for the first time. Use a real fertilizer and not a weed n feed product. I like organic fertilizers, but you can use any one you like.

Randy Lemmon from Gardenline has excellent advice for lawn care in the Houston area:
https://ktrh.iheart.com/featured/gardenline-with-randy-lemmon/

https://facebook.com/GardenLineWithRandyLemmon/

cd7733, thanks for the links. I had to run off and see who Randy Lemmon is. He's a radio personality in Houston on the topic of gardening. Some of his lawn tips seem almost word for word from the annals of this Gardenweb/Houzz Lawns Forum while other tips are passed down from father to son and which have not proved to be beneficial for most people. For example he promotes rototilling to prepare for a lawn. That is a bad idea for reasons found elsewhere in this forum. Another is recommending specific fertilizers without the benefit of a soil test. And along that line he recommends specific micronutrient amendments without the benefit of a soil test. Finally he cannot find corn meal in Houston. I would suggest there are at least a hundred sources for corn meal in Greater Houston. He's the kind of guy who could benefit from regular participation in a lawn care forum where his ideas are presented, reviewed, discussed, and tuned up. If you follow his advice to the letter, you will not kill your lawn, but you will spend more money and run into a little more hassle than you would if you asked a forum about specific issues you are having with your lawn.