Lambda expression as event handler: How do variable/reference scopes work within lambda expressions?

Question

I think I lack the proper words to google the answer to this topic, so if anyone wouldnt mind giving me a quick run down on how this works:

I got a two dimensional List of buttons and a two dimensional list of arbitrary objects of a Class A. When a button is pressed, I want it to call a function that receives the corresponding object of Type A. I run into an out of bounds error though, probably because the List of A is out of scope (while it still does exist, but seemingly not in the scope of the lambda).

What would best practice look like in such a case? When are the variables used in a lambda expression evaluated? Can I make them behave like smart pointers?

public void loadWorld(World w) {
    for (int i = 0; i < w.ListOfA.Count; i++) {

        for (int j = 0; j < w.ListOfA[i].Count; j++)
        {
            Button btn = new Button();
            
            btn.Pressed += (s, e) => handleVisit(w.ListOfA[i][j]);
        }
    }
}