How to tell a lambda function to capture a copy instead of a reference in C#?

What the compiler is doing is pulling your lambda and any variables captured by the lambda into a compiler generated nested class.

After compilation your example looks a lot like this:

class Program
{
        delegate void Action();
        static void Main(string[] args)
        {
                List<Action> actions = new List<Action>();

                DisplayClass1 displayClass1 = new DisplayClass1();
                for (displayClass1.i = 0; displayClass1.i < 10; ++displayClass1.i )
                        actions.Add(new Action(displayClass1.Lambda));

                foreach (Action a in actions)
                        a();
        }

        class DisplayClass1
        {
                int i;
                void Lambda()
                {
                        Console.WriteLine(i);
                }
        }
}

By making a copy within the for loop, the compiler generates new objects in each iteration, like so:

for (int i = 0; i < 10; ++i)
{
    DisplayClass1 displayClass1 = new DisplayClass1();
    displayClass1.i = i;
    actions.Add(new Action(displayClass1.Lambda));
}