Try this:
List<SoonestDrawDateModel> soonestDrawDateModel = new List<SoonestDrawDateModel>();
var realDrawDates = drawDates.ForEach(x =>
{
soonestDrawDateModel.Add(new SoonestDrawDateModel() { CutOffDayId = x.CutOffDayId, DrawDay = x, DrawDayId = x.DayId});
soonestDrawDateModel.Add(new SoonestDrawDateModel() { CutOffDayId = x.CutOffDayId, DrawDay = x, DrawDayId = x.DayId + 7});
});
var realDrawDates = soonestDrawDateModel.OrderBy(y => y.DrawDayId);
Basically, this does the same as yours, but this iteration is more compacted.
EDIT: It seems I messed up while pasting the code, sorry for that, this should work now, try it and let me know