Is Person A lying, but both Person A and Person C ate the pie?
A said it wasn't me and not C, so if A was lying, then they both had to eat it.
If B were lying, they said they arrived late, but C said they arrived late as well so that would mean two of them were lying.
If C were lying, than That means that B and D were both lying as well.
If D were lying, then C would have been lying as well.
Only A could have been lying so that only one person was lying. C was the only one that didn't talk about themselves, so they could be telling the truth without admitting that they did it.
So I'd say Person A lied and Person A and Person C shared the pie.