There are 2 different ideas of thatch in grassy lawns. The dead grass blades that cover the soil between plants is not a serious thatch issue. The other thatch issue involve the roots and stems growing above the soil simply feeding on the water and fertilizers as they are applied. The problem with this type pf thatch is more severe because there is very little root growing into the actual soil. Your last photo just has some grass and a dark spot on my screen, so a caption of what we are looking at would clarify which type of thatch you are concerned with.

Good suggestion, eaga, but I didn't get lucky with the pages that "The Wayback Machine" had archived. It'd be a bit like finding a needle in a haystack, trying to guess what day the Organic Lawn Care FAQ showed up in the discussions. Unfortunately, the search function wasn't able to find it in the archived pages. Guess we'll just have to hope Houzz gets their act together soon.

@OP - You were getting a late start this year. Likely your lawn will still be covered with weeds this summer. I would encourage you to consider "Lawn Solarization". This process takes 4-6 weeks during the heat of the summer, and will kill all weeds, weed seed, and pathogens in your soil. The nice thing is, there is no chemical residue left over, so next fall when you do your overseed you will be in real good shape. One of the things I like about Organic lawn care, is that it forces you to think outside the box. It's easy to pickup a chemical weed spray, or manage a 4-step program... It takes soil knowledge and a buildup of healthy soil to successfully manage your lawn organically. I always tell people, if your really not into it, managing your lawn organically isn't going to work... Even when you are interested, it can be frustrating! That's why the vast majority of people go to the big box store and just throw around whatever they are selling... it takes effort to submit soil tests, analyze results, and apply compost/grains accordingly. This is my lawn, 6 years, no chemicals. Still not perfect, I have some problem areas, and keep learning more all the time.. but my neighbors finally "Get It".. They thought I was nuts when I told them I don't use per-emergence, weed n' feed, 4-step, ect... Lawn Solarization Instructions

Mine varies. Sometimes yes, sometimes no on my Edgeguard, depending on the size of the alfalfa pellets. The stuff from the pet food store, not so much. Most of the time, the cheap stuff from Tractor Supply (I can't remember the brand offhand, it's in a purple bag) works great.