That is interesting, because I often book my travel via a TA and they always have to handle refunds for me. In this case, the TA is LH.
For a compensation claim or duty of care expenses, you would never involve a TA of course, that would be directly with the airline that had caused the disruption. But I'm not attempting to claim those here.
Incidentally, I did query this with the agent that cancelled my itinerary, she said LH were my only point of contact for a refund.
Thanks for the advice everyone, if I could just get a better response from LH who could explain the process then it would have been completed back in October!