In a large mixing bowl (if using an electric mixer) - or in the bowl of a stand mixer fitted with a paddle attachment - whisk together the allulose, the lime zest, and xanthan gum until well combined. Make sure to break up any clumps of allulose - you can do this in a mini food processor, if you prefer. Add cream cheese the bowl, cream the cream cheese and allulose mixture together until smooth.
Add the lime juice, and vanilla extract. Beat on low speed JUST until smooth - DO NOT overbeat! Gently fold in the eggs, just until well combined.
Pour cheesecake batter into the prepared crust.
Place prepared cheesecake in a larger pan, carefully pour hot water into the larger pan, aiming for it to come halfway up the height of the springform pan.
Form a large “tent” out of a long piece of aluminum foil, as pictured in the post. This will prevent excessive browning - from the use of allulose - while preventing condensation from landing on the top of the cheesecake. Carefully transfer the whole thing to the 325 F oven.
Bake cheesecake for 60-65 minutes, or until the center is mostly set - it’ll wiggle a little if shaken, but shouldn’t be liquid.
Turn the oven off, crack the oven door by a few inches, and let the cheesecake cool in there for another 30 minutes or so.
Remove from the oven. Tilt the foil tent to the side and carefully remove it from the pan, pulling it up and to the side. You want to avoid dripping water into the cheesecake.
Carefully remove the springform pan from the water bath, and the foil from the pan.Run a butter knife along the inside of the pan to loosen the crust from the pan, then allow to cool to room temperature. Transfer cheesecake to fridge, chill for at least 8 hours - ideally overnight.
Garnish as desired, serve cold.