System.Lazy with different thread-safety mode

Only one concurrent thread will attempt to create the underlying
value. On successful creation, all waiting threads will receive the
same value. If an unhandled exception occurs during creation, it will
be re-thrown on each waiting thread, but it will not be cached and
subsequent attempts to access the underlying value will re-try the
creation & may succeed.

Since Lazy doesn’t support that, you could try to roll it on your own:

private static object syncRoot = new object();
private static object value = null;
public static object Value
{
    get
    {
        if (value == null)
        {
            lock (syncRoot)
            {
                if (value == null)
                {
                    // Only one concurrent thread will attempt to create the underlying value.
                    // And if `GetTheValueFromSomewhere` throws an exception, then the value field
                    // will not be assigned to anything and later access
                    // to the Value property will retry. As far as the exception
                    // is concerned it will obviously be propagated
                    // to the consumer of the Value getter
                    value = GetTheValueFromSomewhere();
                }
            }
        }
        return value;
    }
}

---

UPDATE:

In order to meet your requirement about same exception propagated to all waiting reader threads:

private static Lazy<object> lazy = new Lazy<object>(GetTheValueFromSomewhere);
public static object Value
{
    get
    {
        try
        {
            return lazy.Value;
        }
        catch
        {
            // We recreate the lazy field so that subsequent readers
            // don't just get a cached exception but rather attempt
            // to call the GetTheValueFromSomewhere() expensive method
            // in order to calculate the value again
            lazy = new Lazy<object>(GetTheValueFromSomewhere);

            // Re-throw the exception so that all blocked reader threads
            // will get this exact same exception thrown.
            throw;
        }
    }
}