In Iowa and Nebraska it's too late to sow grass seed now. The only
possible exception would be to use a fast germinating variety like an
annual rye grass to give quick cover if you had bare soil. But the
question posed is for overseeding an existing lawn and now is too late
for success. Seed sown now will start to germinate and not have enough
time to get established before winter and most of it will likely die.

The best time to overseed is Sept or early Oct. The next best time is
early Spring, so at this point, I would plan on doing it in the Spring.
And the best way is to rent a slice seeder, which you can do for abot
$45 for a half day and transport in an SUV. That puts the seed into
the soil in grooves that it cuts and will give excellent germination
with minimal work. In the meantime, get the soil tested and adjust the
PH, if needed. Figure out what kind of quality grass you will be using
and how you will keep it moist for several weeks while it germintates.