Just use the Concatenation method. That's really what you're doing. You can also use the List constructor that takes an IEnumerable.
var soonestDrawDateModel = new List<SoonestDrawDateModel>( drawDates.Select(s => new SoonestDrawDateModel() { DrawDay = s, DrawDayId = s.DayId, CutOffDayId = s.CutOffDayId, }) .Concat( drawDates.Select(s => new SoonestDrawDateModel() { DrawDay = s, DrawDayId = s.DayId + 7, CutOffDayId = s.CutOffDayId, }) ) .OrderBy(b => b.DrawDayId))