While creating the buttons, you could implement the handler as a lambda so you get access to the context for free. Or you add a dictionary that maps the button to the context you need in a handler method:

public class Presenter
{
private readonly View view;
private readonly Model model;
private readonly Engine engine;
private readonly Dictionary<object, Item> itemMap = new Dictionary<object, Item>();

// example 1
public void LoadFromModel_EventHandlerLambda()
{
foreach (Item item in model.items)
{
var button = new Button();
button.Pressed += (o, args) =>
{
engine.GenerateInformation(item.Foo);
model.DoAction(item.Bar);
button.IsEnabled = false;
};

view.ButtonName.Add(button);
}
}

// example 2
public void LoadFromModel_EventHandlerMethod()
{
foreach (Item item in model.items)
{
var button = new Button();
button.Pressed += OnButtonPressed;
itemMap.Add(button, item);
view.ButtonName.Add(button);
}
}

private void OnButtonPressed(object sender, EventArgs args)
{
Item item = itemMap[sender];
engine.GenerateInformation(item.Foo);
model.DoAction(item.Bar);
((Button)sender).IsEnabled = false;
}
}