The only way to know if you need lime, and what type you should use, is by getting a proper soil test. (www.loganlabs.com) You can add lime almost any time, but generally not at the same time as synthetic fertilize. Space them a few weeks apart. Fertilizing shouldn't really be done in the middle of summer, even though you are in Northern MI. Wait till the heat and humidity break. Weed killers can be used when temps don't rise above whatever they recommend on the label, as it can harm heat stressed grass.

Thank you!