I'm not sure which I am more disgusted with.
Unless you are having seriously cold temperatures this early, there is absolutely no problem with putting in a lawn now. You didn't say whether you mean seed or sod but it really doesn't matter but you can go a little later with sod because you are not trying to germinate anything but just getting roots established, i.e. basically just transplanting.
In most areas, it is against the law to leave bare soil exposed. There are state laws and FEDERAL regulations regarding this. I would suggest checking this with your local codes office that handles eroision and sediment control issues. Beyond that, I don't want to address Ohio law from Georgia.
This link will give you a starting understanding-