There is something wrong with this story.....
1) Why would this person check the bags twice? Even if they were seperate tickets, they would still be able to check them straight through.
2) Why would the original penalty not apply to the entire segment?
3) If this were truly a paid F fare I very very strongly doubt that even LH would have charged this much. For the self righteous out there, yes there are limits that have not been changed since 1929, and if this were a paid ticket no airline would have problems with this amount of luggae assuming that each piece was under 30kg.
4) IF this story is true, AND the ticket was paid, inform your friend in the future if this were to ever happen again to either request that the airline either endorse the ticket to any other carrier, or better yet that they downgrade the ticket to a business class fare and refund the difference - offer to pay the penalty out of the difference - No airline will want to do either.