Should thread-safe class have a memory barrier at the end of its constructor?

Lazy<T> is a very good choice for Thread-Safe Initialization. I think it should be left to the consumer to provide that:

var queue = new Lazy<ThreadSafeQueue<int>>(() => new ThreadSafeQueue<int>());

Parallel.For(0, 10000, i =>
{

    else if (i % 2 == 0)
        queue.Value.Enqueue(i);
    else
    {
        int item = -1;
        if (queue.Value.TryDequeue(out item) == true)
            Console.WriteLine(item);
    }
});