Something is killing the grass in that picture. You need to figure out what it is. Common issues include fungal infections, insect damage or soil nutrient inbalance issues.
Dig around and see if you can figure out what is cause the grass to die. If it's an insect, identifying the insect can help you figure out how to control it. If it's a fungus, planting resistant species/varieties can eliminate the issue. For the soil nutrients sending a sample into a soil lab is relatively cheap and gives you an idea of what might be wrong.
The weed is buckhorn plantain. It's a perrenials that you have to remove the entirety of its roots (almost impossible). It's relatively easy to kill with a well timed application of 2-4D.
https://turf.purdue.edu/buckhorn-plantain/
It does produce a massive amounts of seeds that can remain dormant for decades. So it will likely keep popping up for quite a few years.
