Due to multiple factors, expect to potentially pay more when booking in January. For low rates, June can be a great choice for travel to Lubbock. Flights to Lubbock from Minot in June are about $259 on average during June, but can be found for as low as $95.
Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Minot to Lubbock as you normally would.