Thanks all. Here's what happened:

1. My friend called the US LH hotline and submitted the medical docs via email as instructed.

2. I called the US LH hotline, and was told to submit medical documents via email. They "promised" that the email team would review the docs before departure. When I asked what to do if they don't review the docs prior to departure, I was simply told "they will." (This was incredibly exasperating.) They were apparently unable to cancel, even without a refund, until the documents are reviewed.

3. I called the Germany LH hotline and selected the option for service in English. I was told the same thing as (2), but I held my ground. After ~40 min, the agent suddenly said that she looked at the ticket and a full refund was approved. I have no idea why she didn't say that at the start of the call; I gave her the record locator within the first minute. She promised a refund within 7 days.

(Interestingly, the German hotline's IVR says they'll serve you faster in English than German, probably due to outsourcing, but I digress...)