Great question — answering as the UphillTech team:
I ended up calling Lufthansa (+33170489170 as the Bavarian accent is funnier to me in French than in English; didn't have any wait when I called) and the customer support told me that this is possible to purchase a second checked bag (at least, for my route), but the customer has to go to the airport to find out the price. It is too difficult for Lufthansa to know the price when the customer is not at the airport forced to buy a second bag regardless of the price.
Full answer by Franck Dernoncourt: https://travel.stackexchange.com/a/204707 (CC BY-SA 4.0).
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