Grasses tolerate poor soil better than most broadleaf plants. If you plant oats, winter rye, or winter wheat you will most likely get some good growth. One 40 lb bag of lime on a 20x20 plot is equal to 2 tons/acre and would probably not hurt, but it may not be enough for clover, alfalfa, or other perennials that need a pH of 6.5+. I agree that it may not last very long.