How do I dynamically add properties to object using LINQ

You can not dynamically add properties to classes. I can see a couple of way you could possibly get the desired result.

Simplest would be to amend you classes as

public class Author
{
    public int Id { get; set; }
    public string Name { get; set; }
    public List<Book> AuthorBooks { get; set; }
}

public class Book
{
    public string Title { get; set; }
    public string Isbn { get; set; }
}

However this would give you a slightly different structure on your JSON

The Other way would be to use an ExpandoObject, providing you are using .net.4.0 or above. ExpandoObject allows you to add properties as it is based off the Dynamic class.

You can get more information here https://blogs.msdn.microsoft.com/csharpfaq/2009/09/30/dynamic-in-c-4-0-introducing-the-expandoobject/

Hope this Helps

Edit

You could try something like this

FooList.ForEach((x) =>
            {
                //Define a new expando
                dynamic NewClass = new ExpandoObject();
                NewClass.Id = x.Id;
                NewClass.Name = x.Name;
                //Get the relating Bar Record
                BarList.Where(b=> b.FooId == x.Id).ToList().ForEach((b) =>
                {
                    NewClass[b.Title] = b.Count;
                });
                //This bit Depends on how you want the Json
                using (TextWriter writer = System.IO.File.CreateText("YourFilepat/Here"))
                {
                    var serializer = new JsonSerializer();
                    serializer.Serialize(writer, NewClass);
                }

            });

The JsonSerializer is from Newtonsoft.Json

Have you tried using anonymous types?

var foos = new List<Foo>{
    new Foo{Id = 1, Name = "Grapes of Wrath"},
    new Foo{Id = 2, Name = "Shantaram"}
};

var anonObject = from f in foos
                    select new
                    {
                        Id = f.Id,
                        Name = f.Name,
                        Garden = 6
                    };
var serialized = JsonConvert.SerializeObject(anonObject);
return serialized; //[{"Id":1,"Name":"Grapes of Wrath","Garden":6},
    //{"Id":2,"Name":"Shantaram","Garden":6}]

Mind you that anonymous types cannot cross the function boundary, so you'd have to create your dynamic properties and serialize in the same function.

Alternately, you can just create the new type like this:

public class FooBar
{
    public Foo Foo { get; set; }
    public List<Bar> Bars { get; set; }
}

And this guy can move everywhere, has all the properties you need, won't need to be changed every time you change Foo or Bar, and will cleanly serialize.

If you are looking to dynamically add a property to an object this could be a solution.

This is what has worked for me, I also had a concern and it was what happened with those domain objects that had many properties, the maintainability for any changes in the object was absurd, I managed to build an implementation with LINQ - ExpandObject - Reflection, which helped to keep my object dynamic and only add the additional properties that my view logic required.

var expandedModel = FooList.Select(x =>
                    {
                        dynamic expandObject = new ExpandoObject();
                        expandObject.NewProperty= $"PropertyValue";
                        foreach (var property in x.GetType().GetProperties())
                        {
                            ((IDictionary<string, object>)expandObject).Add(property.Name, property.GetValue(x));
                        }
                        return expandObject;
                    }).ToList();