I assume you've used one Bluegrass Type....instead of a bluegrass mix...(there is more than one type bluegrass) and if you bought a seed MIX, then possibly what you have is a type that has its good side....and a bad side---possibly one or more of the mix is not drought tolerant.
I'll also assume that last season when the drought hit, you didn't bother taking up the slack by watering.
Once the soil dried out, it doesn't take long for grass roots to ...first grow short--then as more summer heat hits it, it dies. Nothing strange about that.

You might decide to instead plant a more tolerant seed mix of bluegrass accompanied by fescue and a perennial ryegrass so that you stand a better chance of defence against droughts.

Now....what to do. I would suggest you do a good hard raking. First rake in the direction north----to south.
Remove all the dead stuff...don't worry if some grass is torn up with it....it wouldn't have survived long anyway....then
rake hard east to west. This cross raking will open the ground to moisture.....if its not too compacted.
If you feel the ground IS compacted, then I suggest AERATING....
then give the area wholesale overseeding with a starter fertilizer.

Good grass seed will do well in poor soil.
Poor grass seed wont do well in the best of soil.
So, buy the best seed you can afford.

Follow the requirements of seeding a lawn. Make sure to sprinkle twice a day for the first week, then once a day for the next week, then twice a week for the next couple weeks...rain notwithstanding.

Next fall, spread 1" of compost over the whole area. This will do an important thing: ingests organic matter into the soil which will help retain moisture.
Every spring, repeat this.....1" of compost (or composted cattle manure) over the area. No need to dig it in...the worms that will come and stay, will come up and take it down.
The grass will be encouraged to grow---its better than fertilizer...but put the lawn on a schedule of fertilization as the lawn requires.

Good compost isn't cheap....if you cant make your own, then get estimates on how much you will need and how much it costs from local soil dealers.

To estimate how much soil to buy....simply measure the area's length X width...in feet....multiply that figure by depth in inches...1"....then multiply that figure by 3 and divide by 1000. (move the decimal 3 places to the left)
That will give you exactly the number of cubic yards of soil you will need.

This actually started happening 2 years ago. I am a stickler when it comes to watering the yard, however last year we were under water ban for most of the summer.

I regularly aerate the lawn as well and don't believe that it is compacted at all. I have done soil tests and have also made sure to add gypsum each year as well.

Regarding the repair, would dethatching with the dethatching blade you can add to your mower do any good?

I've never had any luck over seeding - with the either the best or worst seed, but I was thinking about using this dethatching method and then slit seeding the new seed.

I really want to get rid of these clumps though.