So on full flights (8 pax) where each person has one main course, does LH really throw away 24 meals each flight? Assuming 4 choices.

While BA could stock a few more of each option, some relatively basic statistical modeling could surely save LH quite a bit, if the above is true. No need to stock 8 of an option if, for example, 99% of the time not all 8 are needed.