C# Singleton Thread safe variables

I have referred to Jon Skeet's article here (http://csharpindepth.com/articles/general/singleton.aspx), the sixth version.

However, I have some private variables that I want initialized once, and be used by methods in this supposedly singleton class. I initialized them in the private constructor, but soon found out, that they are null when invoking the methods, in a multi-threaded scenario (Task.Run).

When debugging, I observed that the private constructor doesn't called twice (which should be) when I call out for an "Instance", and so I assume that my private variables, shouldn't be null at that point in time already (succeeding "Instance" calls).

Any idea on how should I declare, initialize, and use these variables?

public sealed class Singleton
{
    private static readonly Lazy<Singleton> lazy =
        new Lazy<Singleton>(() => new Singleton());

    public static Singleton Instance { get { return lazy.Value; } }

    // my private variables
    private readonly string _plantCode;

    private Singleton()
    {
       var appSettings = ConfigurationManager.AppSettings;
       string _plantCode = appSettings["PlantCode"] ?? "Not Found";
    }

    public SomeMethod() 
    {
      var temp = _plantCode; // <== _plantCode becomes null here!
    }

}