Their letter says they've paid. It and its Third Part Authorisation are nonsense because you cannot appeal as you don't have a PCN in your name. A so-called Third Party Authorisation letter cannot circumvent the regulations.
But you could play a straight bat based upon their written authority to act on THEIR behalf. You have plenty of time. But first, what is your relationship with the lease company and are you prepared to drop them in the mire?
Armed with their letter of authority you could ask that their payment be rescinded and say it was made in error and then make representations on their behalf or, if you have the necessary documents, you could make reps effectively to transfer liability to you and start the process with a fresh PCN.
What's your pleasure?