I flew several times with lufthansa but the problem is the same to all the other fly companies I went trough.
The real issue exist between the flight attendant and the airport attendant.
Usually there are companies that let you bring a guitar or bass as carry on baggage and let you put it in the flight attendant closet on the airplane. The real problem come when a ground attendant let you (rare case now) bring the bass as carry on baggage and when you arrive on board the flight attendants don't allow you to bring in with the consequence to send it, just with the gig bag together the regular luggage, and that is a thing you don't want ;-)
Honestly I never heard about book ad additional seat for a musical instrument, what I can suggest you is check your bass with a good case.
I found years ago the solution with the SKB Ata roto case, usually I check it just as regular luggage, some low cost companies make you pay an additional cost for that, but with traditional companies as Lufthansa just give it the chance with a regular fly tickets.
Cheers. www.enricogaletta.com on youtube on twitter study with me