Don't forget that even healthy cool season grass will look a little sad during the hot summer months. Don't waste your time and money on trying to fertilize with tea right now. In fact, I agree with Paul that its too much work for the results. As with many things, less is more.
If your lawn is largely bare dirt, I'd suggest placing a layer of mulch from an organic source. Make sure it is organic. Many sources of mulch include rubber tires, treated lumber
pallets, and other toxic waste. Don't use those. My first big attempt at soil improvement involved tilling the sod under. With what I learned from that, I'd suggest not tilling. But after leaving that area bare for awhile, I discovered that the condition of the soil was rapidly getting worse and not better from the amendments I had added. That was lesson number two actually. The amendments are good, but there is one single thing I think turned my
project from disaster to recovery. That was laying mulch over the dirt. The mulch regulates and moderates soil temperature and moisture. These two things make the worms, microbes and insects happy. Happy fauna for a happy lawn, ahhh. Excuse the pun. The mulch also breaks down and enriches the soil.
My suggested cheap, and lazy way of doing this is simple. It's like Paul says: Mow high, leave the clippings. I would also add that I let my lawn get a bit over grown a couple times a year to help get a good mulch layer. Not too much as to clog the mower, but
enough to build some biomass in one mowing. You know what's used to grow your mulch, so you know its good. Remember the part about making sure its organic? Plus, you get free mulch, spread for you on your lawn. If you get some good spots growing while others are bad, maybe bag or rake these good spots every third or fourth mowing and spread the clippings on the bad areas.
Next, what's your feelings about clover? I personally love it and let it grow as it wishes in my lawn. Clover is a legume. This means its gets happy with a certain bacteria called rhizobium. The bacteria pull nitrogen from the air and makes it into plant food, while the clover makes sugar and feeds it to the rhizobium. Win-win. The same nitrogen plant food made by the rhizobium is also available to your grass. Win-win-win. Yay! Go Team! Get some white clover seed (or similar legume suited to your area) and throw it around. Or better yet, if you already have clover, encourage it to grow and spread. Why waste time and money on buying and spreading seed when you already have it?