Thank you for your (continued) question.  Let's talk first about thatch, a layer of grass roots and stems on the soil surface that accumulates faster than it decomposes.  Some thatch is good and not a problem until it becomes thicker than 1/2" when it creates a favorable place for pests and diseases.  Removing excessive thatch is most easily done with a de-thatching machine, but this is rough on the grass, so is best done in the early fall.  Your photos don't lead me to believe you have excessive thatch.  You need to check the thatch thickness in your lawn.  More info in the attached links:
Managing Thatch In Home lawns-ILL - select the 'thatch' tab, but read other articles as well
Managing Thatch in Lawns-PSU
Core Aeration & Dethatching of Lawns-MSU
Core aeration has benefits in relieving soil compaction, thatch and allowing more access of air and water to turf roots.  Core aerate the whole lawn.  Adding organic matter (compost) and seeding after core aeration is beneficial to the lawn, especially when done in the early fall.  More info in the attached links:
Core Aeration of Lawns-MSU
Core Aeration of lawns-Illinois
Core Aeration of Lawns-Iowa St
I recommend starting the addition of extra phosphorous (P) and potassium (K) before core aeration or reseeding.  Your lawn is starving for these essential macronutrients and can't be robustly healthy without them in sufficient amounts.  In addition to seeding after core aeration you can follow the steps in the lawn renovation articles I attached to the previous email sent to you to thicken your turf, but first increase the P & K levels.  The root cause (pun intended) of your lawn's decline is poor fertility due to lack of P&K, correct this problem before treating for any suspected diseases.
One other thought....looking at your photos I wonder if you might have a grub problem, which would only worsen the fertility problem.  The link to the attached article is a very good instruction set on 1) checking for grubs in the lawn (do this) and 2) reducing the grub population, if excess quantities are found.  And it can be done simultaneously with increasing the macronutrients.   How to Choose & Apply Grub Control Products-MSU