I recommend the following:
1) If not done so already, get the current soil pH. If you got the pH on the ground while it was covered by native plants, note that clearing it will generally result in dropping pH further (clearing typically results in increasing acidity unless you burned it, and then you may see a slight increase).
2) It's August - after getting the current pH, skip the lime and plant the crop that matches the soil type and pH.
3) Contact your local QDMA, or contact the Ohio State U extension office, and get a list of possible crops you can plant immediately. You'll be surprised at how many choices you'll have available.
I'm also assuming you want to plant a killing plot for this fall or an over-winter plot, and in that case you should really get either planted now. You're at the time when you need to plant, and I say this because (at least in my area of SW Michigan) once the critters find a new late summer food plot they tend to either ignore it or hit it heavy, and hitting it heavy often requires overseeding/replanting to make sure it establishes for late fall and/or winter. If you're doing food plots for next year, then disregard...
4) If you want/need to increase pH (making the soil more basic) for a specific crop you want to try, then add the lime and let it leach over the winter - as other's have said, it will take months to see true effects on soil pH.
Personally, you're in the MIdwest and therefore regardless of the pH or soil type, you probably have an 80% or better chance that you can throw a clover mix on it and grow a decent crop for the late summer/fall. That goes against the specs, and I'm sure a few people on here will tell me I'm crazy, but in my area I've found a good clover mix can grow relatively anywhere (pasture, swamp, light, dark, etc) and the deer and other herbivores will use it heavy...