Real Estate Law
Have Real Estate Law Questions? Ask a Real Estate Lawyer.
I will try and help. Much of this would depend on the terms of your lease, but in general your landlord is required to notice if you intend to leave. That gives them the opportunity to find a new renter and not lose a month of rent (or more). Can you be sued? Yes. Will they? Not something we can determine here. You did not indicate what state your are located in, so I cannot determine if specific laws cover this situation.
I hope this helps.
Again, often a lease, if not renewed, converts by its terms to a month to month tenancy on the terms of the lease. Most leases and in this case Ohio Rev. Code Ann. § 5321.17 requires a 30 days notice on a 30 day month to month tenancy. So yes, they can bill you for October since you failed to give the required notice.