Effects that increase or reduce the cost to cast a Trap will apply to whichever cost you chose to pay.

Casting a Trap by paying its alternative cost doesn't change its mana cost or mana value. The only difference is the cost you actually pay.

If both targeted lands are illegal targets by the time Lavaball Trap resolves, the entire spell doesn't resolve. No creatures are dealt damage.

You may ignore a Trap's alternative cost condition and simply cast it for its normal mana cost. This is true even if its alternative cost condition has been met.

You may target any two lands, not just ones that entered this turn.

All creatures are dealt damage, not just ones controlled by the targeted lands' controller(s).