A few years ago I had to fly to Washington DC for one night on a trip paid for by the US government. As they would only approve a coach ticket, I took me more than 10 days of email correspondence to convince them that the business class ticket that I had found, which was cheaper by ~25% (!), would actually save them money. Mind you, that was not on LX, but another major European airline; still air fares are often a bigger mystery than anything written by Agatha Christie.