Agree with bob64, kill the lawn before sowing little bluestem. How much shade does the side yard get? With trees, shrubs and house all adding to shade, you may not able to sustain little bluestem. LBS will grow in oak savanna, but that would be about 20% shade at most.

What you might be seeing is thatch, old dead grass that is acting as a mulch and will be feeding the Soil Food Web. Some, 1/2 inch, of thatch is not a problem, but much more can be. When you mow do you collect the grass clippings or do you mulch mow?

Yes, shrubs'n'bulbs, we seem to be living in completely different climates, horticulturally. So much for applying the zone system here (we've both put 8-9). The Mediterranean characteristics of the climate have been exaggerated. The reason for the drought was not the hot summer (we had loads of rain in May and August) but the very dry and reasonably cold winter right up to the end of March. Spring happened very rapidly in April, then we switched straight over to a very long summer. The Mediterranean aspects are the shut-off in mid-summer and the warm Indian summer/early autumn. Plants (including lawns) have simply been catching up. I thought they mostly had some kind of trigger which switched off when light levels or daylight hours fell below a certain threshhold, but apparently not - and certainly not grass.

Where do you live? What kind of grass do you have? - Dethatch No. Thatch, if you have it, is the least of your problems. - Cut the grass short Oh heck no. Always mow at the mower's highest setting or nearby. - Scarify Scarify is something you do to seeds that need to be roughened up. What does it mean in your context? - Aerate Probably not. Wait until you have the major issues resolved. - for the muddy areas, apply triple mix soil to flatten and level the lawn Not yet. Assuming you have low spots, you need to address those. Fixing those should get rid of the muddy parts. - overseed / over the mud spots, I will apply more seed and Wait for seeding (preferably until September), but until you have the bumps and dips sorted out. - put triple mix soil on top of seed No. You probably already have too much soil in the yard. Almost nobody is short of soil. There are tons of people who put 1/4-inch of topsoil on the yard EVERY year. Well, in 4 years that's an inch of soil you don't need. - Rake and spread the soil around NO! No more soil. - add water NO! You already have a water problem. I live in Texas and have not watered my lawn yet this year. Well, a little on the southern bank, but then it rained, of course. The big thing is to identify any drainage issues. Water should drain away from all the buildings and out to the curb or a ditch somewhere. If you have low spots anywhere, or if you have soil higher than the concrete walkways or driveways, then you have too much soil already. Scraping it up and hauling it away is a huge deal that I've rarely seen done, but that solves so many issues. Fixing the drainage will NEVER involve tilling the soil. It might involve scraping surface soil away to form a swale or ditch, but rototilling is never in the solution to drainage. Rolling is similarly useless in profiling the surface. It looks like your yard is bumpy mostly from lumps of grass interspersed with dead spots. I would not jump to any conclusions about the soil being bumpy until you get an even stand of grass.