The first page lists various aircraft that do and do not have first class by airline. Under LH you have the 346 (A340-600) as not having first class; however, most of the 24 346's that LH has DO have First. Only a few don't. Many of the flights out of Munich that are listed under LH are with the 346. Unfortunately, there's no easy way to tell from the timetable, since LH doesn't differentiate according to Seatguru.