Put ¼ cup cold water in a small bowl and sprinkle the gelatin on top. Set it aside for a few minutes while the gelatin "blooms," or absorbs the water.
In a small saucepan, stir together the other ¾ cup of water, ⅓ cup lime juice, ¾ cup sugar and bring it to a simmer over medium heat. You'll want to stir or whisk until the sugar completely dissolves.
Add the gelatin to the saucepan, and stir until the gelatin has fully dissovled.
Pour the mixture into a bowl and set it aside to cool at room temperature, until it's about the same consistency as egg whites. You can put the bowl in the fridge to speed the process up a little, but be careful that the gelatin doesn't fully solidify!! The gelatin mixture needs to be about the same consistency as an egg white.
While you're waiting for the gelatin to cool, whip the egg whites to soft peaks with an electric mixer. The egg whites should be light and foamy and should form little peaks that quickly fall over when you lift the beater out of the bowl. Since you aren't going to cook these egg whites, making sure they're pasteurized is going to be key.
Add the cooled gelatin mixture to the bowl with the whipped egg whites and continue to beat to stiff peaks. The mixture should be smooth and shiny, and should form little peaks that stand up when you lift the beater out of the bowl.
Whip in the vanilla extract.
Transfer the mixture to the prepared pie plate and spread evenly on top of the baked graham cracker crust.
Put the pie in the refrigerator for about four hours until the gelatin sets up to a slice-able firmness.
Sprinkle lime zest on top for color and decoration.