Simple foreach adding to a list

If you don't have access to changing the constructor, you could opt for the following syntax:

foreach (var item in drawDates)
{
    var sdModel = new SoonestDrawDateModel() {
         DrawDay = item,
         DrawDayId = item.DayId,
         CutOffDayId = item.CutOffDayId;
     };
    soonestDrawDateModel.Add(sdModel);

    # Alternatively, do it directly in the Add method
    soonestDrawDateModel.Add(new SoonestDrawDateModel() {
         DrawDayId = item.DayId + 7,
         CutOffDayId = item.CutOffDayId,
         DrawDay = item
    });
}

This is not Linq syntax, but it is still a rather neat way of adding newly created objects without (in the alternative method) using temporary variables. It also connects the initiliasation and default setting of public properties/variables neatly into a block of its own.

What you're doing here, essentially, is creating two Model items for each item in your source list, and storing them in a list. Here's a somewhat contrived usage of the SelectMany LINQ function which flattens a hierarchical list:

drawDates
  .Select(dd => new SoonestDrawDateModel[2]  // create a 2-item array for each item.
                 { 
                   new SoonestDrawDateModel 
                    { 
                      DrawDay = item, 
                      DrawDayId = item.drawDayId,
                      CutOffDayId = item.CutOffDayId
                    },
                   new SoonestDrawDateModel 
                    { 
                      DrawDay = item, 
                      DrawDayId = item.drawDayId + 7,
                      CutOffDayId = item.CutOffDayId
                    } 
                }) // end of Select method.
 .SelectMany(items => items) // flatten collection of arrays into one collection.
 .OrderBy(x => x.DrawDayId); // order by.
 .ToList() //convert to a List<SoonestDrawDateModel>.

What we're doing here is creating a 2-item array or each Draw item, meaning we have an IEnumerable<SoonestDrawDateModel[]>, then use SelectMany to take all the members of each SoonestDrawDateModel[] and flatten them into one big IEnuemrable<SoonestDrawDateModel>, which we then sort and return.

You can simplify the syntax by extracting the main creation block into a method:

private SoonestDrawDateModel[] CreateDateModelPair(DrawItem item)
{
    return new SoonestDrawDateModel[2]
    { 
     new SoonestDrawDateModel 
     { 
        DrawDay = item, 
        DrawDayId = item.drawDayId,
        CutOffDayId = item.CutOffDayId
     },
     new SoonestDrawDateModel 
     { 
        DrawDay = item, 
        DrawDayId = item.drawDayId + 7,
        CutOffDayId = item.CutOffDayId
     } 
  }
}

then call it with this LINQ call that conveys the intent rather well:

drawDates
  .Select(CreateDateModelPair)
  .SelectMany (dateModels => dateModels)
  .OrderBy (dateModel => dateModel.DrawDayId)
  .ToList();

Or, as @anaximander suggests, an even terser (but less explicit) version that combines the Select and SelectMany calls. It saves a step, but it's less clear that we have two things going on - one to convert the DrawDate to two SoonestDrawDateModels, and another to flatten that list of lists.

drawDates
  .SelectMany (CreateDateModelPair)
  .OrderBy (dateModel => dateModel.DrawDayId)
  .ToList();

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

You can make a constructor that accepts the 3 parameters:

foreach (var item in drawDates)
{
    SoonestDrawDateModel sdModel = new SoonestDrawDateModel(item, item.DayId, item.CutOffDayId);
    soonestDrawDateModel.Add(sdModel);

    sdModel = new SoonestDrawDateModel(item, item.DayId + 7, item.CutOffDayId);
    soonestDrawDateModel.Add(sdModel);
}

in linq that lets you do

drawDates.map(item => new SoonestDrawDateModel(item, item.DayId, item.CutOffDayId))
       .concat(drawDates.map(item => new SoonestDrawDateModel(item, item.DayId + 7, item.CutOffDayId)).OrderBy(x => x.DrawDayId).ToList();

If I were to code-golf this question, I would probably go for something like

//use plural to indicate that this is actually a collection of models
//and not a single model
var soonestDrawDateModels = 
//for every date create model with and without offset
drawDates.Select(date => new SoonestDrawDateModel(date))
         .Concat(drawDates.Select(date => new SoonestDrawDateModel(date, 7)))
         .OrderBy(model => model.DrawDayId)
         .ToList();

I think this solution is not only short, but also pretty readable.

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)
)

Repeated Code

I can see the repeated code, which can be removed by introducing following method:

public static void AddToSoonestDrawDateModel(string day, int dayId, int cutOffDayId)
{
    var sdModel = new SoonestDrawDateModel
    {
        DrawDay = day,
        DrawDayId = dayId,
        CutOffDayId = cutOffDayId
    };

    soonestDrawDateModel.Add(sdModel);
}

After refactoring code should be like this:

var soonestDrawDateModel = new List<SoonestDrawDateModel>();

foreach (var item in drawDates)
{
    AddToSoonestDrawDateModel(item.Day, item.DayId, item.CutOffDayId);
}

var realDrawDates = soonestDrawDateModel.OrderBy(x => x.DrawDayId);

Obviously, it is not LINQ, but it is more neat, readable and less repetitive code.