When you fly one airline but collect miles in another programme, (crudely) the airline that you fly will 'supply' points to the programme that you choose to collect with. If LH chooses to provide only 50% to SQ then SQ can do little about it.

This policy is actually pervasive: NH provides 70% of miles on (I think only) discounted economy fares, SQ has eliminated several discounted economy fares ffrom earning miles altogether (regardless of what programme you collect with).

Some bilateral agreements are even more restrictive (or generous), but at the end of the day, the airline you fly with makes the rules.