The areas that are not hit with the sprinklers are completely, 100% dead...

Im not a turf grass scientist, Jay, but I've been assured that grass
does not die when it gets dry; it just goes dormant and will green up
when rain arrives.

As an aside, I have not watered my lawn for at least 20 years, or
fertilized it, either. It has NEVER in my memory turned brown during
that period, and we've had our droughts in central PA, too. In fact,
we're having one now. Farmers are in serious trouble.

And yet I have to mow it every damn week. I mow it high, 3", and
leave the clippings.

If you regularly water your lawn, especially not deeply enough, it
becomes "hooked" on that watering. Roots seek that shallow water.

If you don't water it, the grass "learns" to send its roots deep,
where there is some moisture even during droughts.

vince norris