The cost-reduction ability of Lumbering Megasloth doesn't change its mana cost or mana value, only the total cost you pay. Specifically, the mana value of Lumbering Megasloth is always 12.

Once you announce that you're casting Lumbering Megasloth, no player may take actions until you're done casting it. Notably, opponents can't remove counters from players or permanents to try to change Lumbering Megasloth's total cost.