The strata manager can (or should) only act as instructed by the strata committee, provided the action complies with strata or any other law. What you could ask them to do is to send out a straw poll sheet outlining the basic arguments for and against lopping, and asking owners to vote.
Alternatively, if an individual owner is affected to their detriment, such as by over-shading, they could commence action at Fair Trading then NCAT to force the owners corp to fix the problem. The point of this would not be to drag the OC to the tribunal, but to make the other owners aware that doing nothing can come at a cost; and if they don’t want to waste money defending a position that a majority may not support, then they should empower the strata committee take the appropriate action.