The spell being cast doesn’t reduce its own cost, even if you’re casting it from a graveyard. At the time the cost is reduced, the spell is on the stack.

Colored costs can’t be reduced by this effect. For example, a spell that costs can’t be reduced by more than .

Locket of Yesterdays reduces only the amount of mana you need to pay to cast a spell. The spell’s mana cost and mana value are not affected.