Long closed Goldfish loan

Antrobus is incorrect.
Different parts of the Goldfish business were sold to different providers. Lloyds Banking Group hold the liability for unsecured personal loans under Goldfish.
Easiest way to resolve this is to make a Data Subject Access request (DSAR) to Lloyds on their website. Alternatively, you can simply walk into a branch with ID and ask them to print out the products you have with them - and they can usually do this at the till or customer service).
I believe that many go the Goldfish legacy loans were sold with PPI (mine certainly was) and like you, Lloyds denied that it existed at first. I then confronted them with the printout and once again they denied it had PPI (even though the product clearly said, "Goldfish legacy loan with Insurance"). Eventually, I had to complain to the FOS.

Perseverance I am afraid is the only thing that will get the Banks to do the right thing! Don't take their first no as an answer as I have had refunds from Santander, Lloyds and RBS on products where they initially said no PPI was sold!!