In your case, best to post a picture.

Here's a picture of the area I'm talking about

You're worried about the area encircled in the faint orange circle, right...not the rest of the lawn??

Yes it looks dead or afflicted by a fungus. Why does the area collect water? I mean obviously it is a low spot but can you bring it up with topsoil or sand so water doesn't collect there? Water can drain across it but it cannot stand there after the rains drain away.

Since there is some green grass in there, there is a chance it will recover. My experience with zoysia would indicate it will not recover this year but might next year if you can get it raised up just enough to keep the water flowing and not back up further into the lawn. Seems like a delicate balancing act.