To convert your C# class into a singleton pattern based on System.Lazy, all you need to do is just adding these two lines of code into your class:

private static readonly Lazy<YourClass> lazy = new Lazy<YourClass>(() => new YourClass());
public static YourClass Instance { get { return lazy.Value; } }

Example:

using System;

namespace YourNamespace
{
    // 1. Make your class as a "public sealed" class
    public sealed class YourClass
    {
        // 2. Add these lines of code
        private static readonly Lazy<YourClass> lazy = new Lazy<YourClass>(() => new YourClass());
        public static YourClass Instance { get { return lazy.Value; } }

        // 3. Make your constructor as "private"
        private YourClass() {}

        // 4. Example methods you want to expose
        public void Foo() {}
        public void Bar() {}
    }
}

And this is how you or other people will use your singleton class:

using System;
using YourNamespace;

namespace ExampleProgram
{
    class Program
    {
        static void Main(string[] args)
        {
            YourClass.Instance.Foo();
            YourClass.Instance.Bar();
        }
    }
}