You can't get a POPLA code until the appeal is rejected. It's pity no receipt was kept and payment was by cash as, in many cases, PE will cancel if you can evidence being a paying customer.
If you are going to try nd get Lidl to cancel it, then go as high up the management food chain. Don't go in and try a lowly customer service person to know how to deal with it. As this is a Lidl only customer car park, they will be able to ask PE to cancel it.
Whatever you do, do not mention that the car was left there whilst the driver went off to do something else. Think of an excuse why it would be parked there for so long. Is there a cafe at this Lidl?
Whilst the location on the NtK simple states Lidl Cathays, it is not really ambiguous as simply entering that in Google maps, comes up with the location. It only works where there is ambiguity such as a town with more than one Lidl store.
Once an appeal is made, they normally freeze the mugs discount and when they reject, they normally give you another 14 days to pay it.