Note LH exceptions!
This is really not as simple as it might seem. Take LH, for example:
LH ticket in coach, for *Gold: 2 * 23 kg
LH ticket in business, for *Gold: 3 * 32 kg
Without *Gold, deduct 1 bag
However: LH now has a "most significant carrier rule". For example: if you fly TATL on UA and have an intra-European connection on LH, UA baggage rules apply - even when you check in with Lufthansa. Basically, you need to count the miles on every carrier for your trip, the carrier with the most miles governs the baggage rules.