What if Aechmea's trying to make the gems as fed up with life as the Lunarians are, so that they too will ask Sensei to pray for them all? Having the Gem ask Sensei to pray for the Lunarians probably wouldn't work, as Sensei doesn't obey the Gems, but maybe he's programmed to pray for the Gems themselves should they ask for it, and maybe his prayer would then release the Lunarians as well.
Mind you, I don't believe that Sensei's prayers would actually solve anything, but the Lunarians seem to believe it would, so the plan could make sense from their p.o.v..