As a general rule, lawn sowing should be initiated when the weather is neither too hot nor too cold. Temperature and the amount of water are two extremely important factors that influence seed germination and healthy growth.
Yes you can plant new grass in the fall. Actually, the first half of autumn is the ideal time to plant the lawn. The soil is still warm, and moderate temperatures, both day and night, encourage rapid germination and the establishment of a strong root system. You may want to look where to buy top dressing for lawns and apply that for added nutrition.
In September and October, the grass is in the active growing period, the risk of extreme temperatures (either too hot or too cold) is low, and rainfall is moderate. Newly planted seeds require consistent soil moisture, and autumn planting offers benefits from this point of view.
If you sow during this period, when winter comes, the lawn will be mature enough to enter the period of passive growth and withstand low temperatures. Rain reduces the chances of the seeds drying out and the need for additional watering. If you do not have an irrigation system, it is recommended to use quality grass seeds, tolerant to prolonged dry periods, to reduce the risk of problems.
Finish planting by irrigating the soil properly, so that water penetrates it and creates a moisture layer.