Doh!
It would have made more sense if I had some other piece of information to inject in, like if you had a database reference that needed to be passed in to the Delete() method.
Then:
AddButton("Delete " + obj.ToString(), () => obj.Delete(db));
Vs. var d = new DeleteHandler(obj, db);
AddButton("Delete " + obj.ToString(), d.DoDelete);
EDIT: fixed