I did manage to get my reservation on LX (Swiss) business one way.
The entire process was by email - no calls, no ticket offices.
I found an email of a closest ticket office from TK website. Asked them if I could come in and do my awards reservation and pay the fees. They offered to do by email instead (after I rejected phone idea - see details below).
So I send them all the flight details, they emailed me two forms (miles and payment) and also asked to add credit card and driver's license scans. That's it.
I found phone agents completely useless. The local ticket office only opens for 2.5 hours, inside an airport in the middle of the day - not worse it. They don't have direct phone to find out if they have a clue how to do it, it is redirected into the main 800 number. The phone people passed me to different places (miles to reservation to customer service - each one dimmer than the other). One suggested to do reservation and pay fees to Swiss directly - Swiss told me that is crazy, which I completely agreed with. That is why email turned out the only way I could get it - after I repeatedly asked them how to get an appointment during the opening hours at the ticket office.