Oats can tolerate poor soil, would probably do OK without the lime if your pH > 5, and they do not need much fertilizer either. If you are in the north, I do agree that winter rye is a better option than oats for the reasons stated. Winter rye also requires little fertilizer and tolerates lower soil pH even better than oats.
Roundup needs at least 1 week to kill weeds, 2 weeks is better for perennial broadleaf plants.