What, EXACTLY, did you put in your representations to LPS? Besides the fact that it is not illegal to stop on double yellow lines (DYL) on the public highway (unless they have the kerb blips), why do you think an unregulated private parking company can penalise you for doing so on private land?
Without seeing the Notice to Keeper (NtK) you received or knowing what you actually said to LPS when you made contact, it is difficult to advise on how you should proceed. The only thing you need to know is that DCBL has absolutely NOTHING to do with this. They are not a party to the contract allegedly breached by the driver. They are completely powerless to do anything except to persuade the low-hanging fruit on the gullible tree to pay up out of ignorance and fear.
Never, ever, ever enter into communication with a useless and powerless debt collector. You can safely shred their letters and use them as master bedding for all anyone cares.
Hopefully, the drivers identity was not revealed when you contacted LPS. It is very highly likely that there isn Keeper liability, but without seeing the appeal you made and the NtK itself, we may never know.
The only saving grace, if the drivers identity has been blabbed, is that no contract could have formed because there is no evidence that the vehicle was parked for longer than the minimum 5 minute consideration period.
So, show us the NtK, redacting only your personal info and leaving ALL dates and times vsible and tell us exactly what was in the comms you had with LPS.