If your lease company has paid both the Parking Charge Notice (PCN) for the airport drop off and the fake Penalty Notice (PN), then, unless the terms of your lease specifically allow them to pay invoices from unregulated private parking companies, you have been screwed royally.
What they should have done is simply transfer liability to you as the Hirer of the vehicle and that would have been the end of the matter for the lease company. Once the liability is transferred, APCOA is supposed to then send a Notice to Hirer (NtH) in your name and you could have easily dealt with this. Nobody who is here receiving advice ever pays a penny to APCOA.
The PCN is very easily disposed of by informing APCOA that, as the Hirer or Keeper, you are under no legal obligation to identify the driver to an unregulated private parking company and as the alleged contravention was on airport land, it is not relevant land and so there can be no Hirer/Keeper liability. APCOA would have cancelled the PCN in response.
As for the fake PN, that is part of a huge extortion racket that APCOA have going on and should be reported to Action Fraud. APCOA cannot issue a Penalty Notice for breach of railway bylaws as they are not the authority that has the statutory powers to do so. Only the Train Operating Company (TOC) or whoever owns the land where the station car park is located, such as Network Rail can issue a PN. Any penalty that is properly issued and then paid, should go to the public purse, not APCOAs bank account.
Any real PN can only be enforced through the magistrates court and that would require the TOC to lay evidence to the court and obtain a summons where it could then be challenged. The burden of proof in a criminal matter is much, much higher than for a civil contractual dispute and must be beyond a reasonable doubt.
Because APCOA has set a fake PN, it is nothing but an "offered contract" that no-one is obliged to accept. Basically, the are using unlawful language in their offered contract that if you bribe them £100, they will not criminally prosecute you in the magistrates court, which they cannot and would not do anyway. The language used in the offered contract is unlawful because it suggests that they have powers that they do not possess and threatens you with criminal liability which simply is not true.
However, this is all moot if the feckwits at your lease company have gone and paid the charges. Your only recourse is to sue them for the amount they have unlawfully taken from you. Check what your lease says about "parking charges". In most cases, they only refer to "fines" or "penalties" from "authorities" or the police.
It really p!sses me off when these companies simple pay speculative invoices from the likes of APCOA or any other unregulated private parking company and then tell the Hirer that it is not their problem anymore. They have breached the CRA 2015 by denying you any opportunity to appeal.
If they collect any payments they have made that you dispute you should have those payments stopped. If by card, make a chargeback. If by direct debit, you dispute it with your bank.
Edit: I have just read back through your previous post. You lease company has been conned into paying the fake PN. You can sue them for any charge they have made to you. They have been conned by the wording on the fake PN. This can be reported to the police for investigation. APCOA have absolutely no authority to issue PNs. The DfT even made this clear in a 2018 response to POPLA where they said they expect any breach of a railway bylaw for a minot parking offence to be dealt with under civil contract law and not bylaw 24.1 which is for more serious offences. Parking offences were decriminalised back in 1999 with the introduction of the Road Traffic Act.
For the airport PCN, when you receive the NtH, just appeal with the following:
I am the Hirer. APCOA cannot hold a Hirer liable for any alleged contravention on land that is under statutory control. As a matter of fact and law, APCOA will be well aware that they cannot use the PoFA provisions because Heathrow Airport is not 'relevant land'.
If Heathrow Airport wanted to hold Hirers liable under Airport Bylaws, that would be within the landowner's gift and another matter entirely. However, not only is that not pleaded, it is also not legally possible because APCOA is not the Airport owner and your 'parking charge' is not and never attempts to be a penalty. It is created for APCOA's own profit (as opposed to a bylaws penalty that goes to the public purse) and APCOA has relied on contract law allegations of breach against the driver only.
The Hirer cannot be presumed or inferred to have been the driver, nor pursued under some twisted interpretation of the law of agency. Your NtH can only hold the driver liable. APCOA have no hope at POPLA, so you are urged to save us both a complete waste of time and cancel the PCN.