Давайте уже добьём эту задачу. Спрашиваю

C# can a private field be initialized lazy through an abstract property?

Отвечает

Yes, a private field in C# can be initialized lazily through an abstract property, but it requires some creative implementation. Since abstract properties do not have a backing field themselves, you can use a private field in the derived class to store the value and implement lazy initialization in the property getter.

public abstract class BaseClass
{
    // Abstract property
    public abstract string LazyProperty { get; }
}
public class DerivedClass : BaseClass
{
    // Private field for lazy initialization
    private string _lazyField;
    public override string LazyProperty
    {
        get
        {
            // Lazy initialization
            if (_lazyField == null)
            {
                _lazyField = "Initialized lazily!";
            }
            return _lazyField;
        }
    }
}

Ну вот, что-то уже похожее на решение, да? Только кто задачу-то решил?