Floris,
It's been my experience that, in Germany, LH does not / will not directly handle group bookings. When I needed to book a group of 12, Lufthansa directed me to contact a travel agent to arrange discount group pricing. The travel agent then works with Lufthansa to make the group booking happen.
In the U.S., LH does handle group bookings directly. We planned a group as small as seven. Handled by
LH Group Sales USA. But, if it's a European departure, it's VERY doubtful that Group Sales USA will offer a competitive fare. They were consistently 1.5x to 3x more than what I could get through a German TA, even without any group discount.