I suspect that the dead areas are those impacted by drought stress over the summer.  Without regular irrigation cool-season turf will go dormant.  If it goes dormant and remains dry for too long over the summer, the crowns of the grass plants die.  When temperatures cool and water is provided again those areas that went dormant but the crown of the plant survives will regrow and green up again. Those areas where the crown died will remain brown.

Its likely the areas in full sun were drier and hotter than those in more shade.  When irrigation was not provided, those areas in full sun dried out sooner, stayed dry longer and therefore were more likely to have plants die.

The areas that were lost due to drought damage will need to be reseeded. Early fall is the best time to reseed new turfgrass.  More information about reseeding can be found in these links:

https://hortnews.extension.iastate.edu/2005/7-13/overseed.html

https://store.extension.iastate.edu/Product/4396 (click the "Download" button in the center of the page to download and open the free pdf file)

For future reference, more information about maintaining lawns during hot dry summers can be found here: https://www.extension.iastate.edu/news/yard-and-garden-watering-home-lawns  

Dead patches in the lawn can be from other issues.  While this situation is likely drought damage, certain diseases, herbicide damage, or warm season grasses, such as zoysia and nimblewill, going dormant can also cause dead patches (or patches that look dead).

Finally, the eastern half of the state has had a big outbreak recently of fall armyworm that can also cause extensive damage to lawns.  More information about this pest can be found here: https://hortnews.extension.iastate.edu/fall-armyworm-control-home-lawns-2021

Further questions can be directed to your local county Extension office. This local resource can be very helpful since they are familiar with trends and issues in your part of the state. Click on this link to get the contact information for the Black Hawk county Extension office. https://www.extension.iastate.edu/blackhawk/ 

Happy gardening!

--Aaron