Answer: Fertilizer is not going to be a cure-all. You would only benefit the existing grass by fertilizing if the soil fertility is low. (Overfertilizing is potentially damaging.) The only way to know that is by running soil tests.
You should run the soil tests in preparation for your fall lawn work. They will tell you whether or not you need to fertilize (and by how much) and also if you need to lime to adjust the pH. It is important to have a suitable pH so the grass can take up and use the fertilizer that is applied.
Lawns tend to grow more slowly in the heat of August so fertilizing now is not that important. A fall application is the most beneficial time of the year.
A new lawn generally is given a fertilizer with proportionately lower nitrogen such as a "starter formulation" and which will benefit the entire lawn. In my experience, lawns usually grow less in August anyway and need less nitrogen then as a result. It would be better to wait until you reseed and fertilize then, using a starter type, and your application will last for the fall growing season that way. Depending on which fertilizer product you use, the slow release formulations should be active for several months.
I hope this helps.
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