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Turn everything to an artifact and shut it down. Lots of stuff can be cast without mana. Black Market will give you mana each round. Shield Sphere should remain a 0/6 wall and not get -1 counters once the lattice is out Once Stony Silence and the lattice is out all lands are artifacts and can no longer be tapped for mana
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Mycosynth lattice won't change anything to shield sphere, it's already an artifact anyway. Tapping a land for mana is not an ability and therefore I don't think it will work with Stony Silence when the lattice is out.
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Stony Silence does work with the lattice. There's a write up about it on the wizards website http://www.wizards.com/magic/magazine/article.aspx?x=mtg/daily/ftl/166
Shield Sphere's ability is triggered, not activated. Kind of a cool idea though.