In first: both are excellent though LX have reduced ground service. NB no F on short haul on either airline.

In business: LX beats LH, more so when traveling alone due to the lack of single seats. There are many reports on this forum so I suggest you read a bit more and ask any remaining, specific questions. On short haul C is pretty much the same on both airlines.

In economy: avoid LX B77W with 10 abreast seating. Again read some of the reports in the site.