Planning this for a Star-rtw, I am tempted to include more (all?) Star-ff-prgrams and qualify in several(all?) ff-programs for the bonus.
The LH promotion (so far the only one which is fully published) 'only' asks for one segment per Star-carrier (no code-shares), no return trips/-tickets necessary (these rules are the same as for 'similar' Star-promotions years ago.
As it is now sure, that in one way or the other, (see the announcement on the StarAlliance-homepage) all Star-carriers will offer similar (minor adjusted, but hopefully with the same time-frame?) promotions, I think the best to really profit from each other is to follow (and contribute to) closely the thread in the Star forum here (and not so much under the individual airlines).