Needlebite Trap

• WWizards of the Coast2009-10-01
  Official Ruling
  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.
• WWizards of the Coast2009-10-01
  Official Ruling
  Needlebite Trap's alternative cost condition checks only whether life was gained. It doesn't care whether life was also lost. For example, if an opponent gained 4 life and lost 6 life during the turn, that player will have a lower life total than they started the turn with — but you can still cast Needlebite Trap by paying .
• WWizards of the Coast2009-10-01
  Official Ruling
  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.
• WWizards of the Coast2009-10-01
  Official Ruling
  Effects that increase or reduce the cost to cast a Trap will apply to whichever cost you chose to pay.

Rulings via Scryfall