Hello and welcome to CAG.
It's very likely that your father won't have to pay these 'fines', but you're going to be doing a crash course with us in how private parking companies work. I hope your father has kept all the paperwork including Lidl receipts? Please ask him not to throw anything away for now.
You did the right thing in contacting Lidl which is what we would have suggested, it's a shame they won't help. I expect someone like ericsbrother will have ideas on how to embarrass them.
Great stuff, is always best practice to check with the court, PPCs have a nasty habit of saying have discontinued but carry on. Interestingly I wonder what would happen if they went ahead, after sending the letter and victim presents the letter of discontinuance to the court after a default?