You won't gain life
As Obeka can be tapped to immediately end its controller's turn, exiling any spells and abilities from the stack by doing so, Obeka can be activated when this game-loss trigger is on the stack, negating it completely and allowing Last Chance and Final Fortune to function as two-mana extra turn spells with no drawbacks
In fact, experts believe we may be approaching an event horizon where more Magic cards are printed than there is money in the world to buy them, at which point we'll see economies crumble, governments topple, and trading cards become the only accepted currency across the globe (keep your rare MTG cards close
This makes it painfully easy to get more use out of your creatures abilities, and is so easy to break that its actually banned in Commander
The Metalcraft restriction initially looked balanced on paper, but Artifact decks consistently enabled it with ease
This is why even when you don't cast her she still has good odds on winning the game