Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from California to Lubbock as you normally would.
Due to multiple factors, expect to potentially pay more when booking in January. For low rates, August can be a great choice for travel to Lubbock. Flights to Lubbock from California in August are about $371 on average during August, but can be found for as low as $168.