I'm putting this in a separate answer because your EDIT makes your question really different.
I'll probably extend this answer later as I'm in a bit of a hurry to get to a client.
Your edit indicates you need to rethink about value types, reference types and the effect of var, out, const and no parameter marking at all.
Let's do the value types thing first.
The values of value types live on the stack and have a copy-on-assignment behaviour.
(I'll try to include an example on that later).
When you have no parameter marking, the actual value passed to a method (procedure or function) will be copied to the local value of that parameter inside the method. So the method does not operate on the value passed to it, but on a copy.
When you have out, var or const, then no copy takes place: the method will refer to the actual value passed. For var, it will allow to to change that actual value, for const it will not allow that. For out, you won't be able to read the actual value, but still be able to write the actual value.
Values of reference types live on the heap, so for them it hardly matters if you have out, var, const or no parameter marking: when you change something, you change the value on the heap.
For reference types, you still get a copy when you have no parameter marking, but that is a copy of a reference that still points to the value on the heap.
This is where anonymous methods get complicated: they do a variable capture.
(Barry can probably explain this even better, but I'll give it a try)
In your edited case, the anonymous method will capture the local copy of the List. The anonymous method will work on that local copy, and from a compiler perspective everything is dandy.
However, the crux of your edit is the combination of 'it works for normal parameters' and 'who guarantees that the reference is still pointing to an alive object whenever the anonymous method is executed'.
That is always a problem with reference parameters, no matter if you use anonymous methods or not.
For instance this:
procedure TMyClass.AddObject(Value: TObject);
begin
FValue := Value;
end;
procedure TMyClass.DoSomething();
begin
ShowMessage(FValue.ToString());
end;
Who guarantees that when someone calls DoSomething, that the instance where FValue points to still exists?
The answer is that you must guarantee this yourself by not calling DoSomething when the instance to FValue has died.
The same holds for your edit: you should not call the anonymous method when the underlying instance has died.
This is one of the areas where reference counted or garbage collected solutions make life easier: there the instance will be kept alive until the last reference to it has gone away (which might cause instance to live longer than you originally anticipated!).
So, with your edit, your question actually changes from anonymous methods to the implications of using reference typed parameters and lifetime management in general.
Hopefully my answer helps you going in that area.
--jeroen