In a large mixer bowl or stand mixer bowl, use the beater attachment to cream the cream cheese until soft and smooth. You're not trying to add air, just soften the cream cheese. Keep the mixer on low speed. Scrape the bowl and the beater.
Add the granulated sugar and lime zest, mix until no lumps of cream cheese remain. Scrape the bowl and paddle attachment again. Add the sour cream, scrape the bowl and paddle attachment again.
With the mixer running on low speed add the eggs/yolk in 2 batches, Scrape the bowl and paddle attachment between batches. Add the vanilla and lime juice (2 tablespoons) and mix until combined.
Divide the batter evenly between the two prepared pans. Set the pans into slightly larger pans and pour an inch of warm water into the larger pan.
Bake until the center of the cheesecake is set (see note), about 15 minutes for the layer with no crust and about 20-25 minutes for the layer with the crust.
Allow the layers to cool to room temperature then place the pans in the freezer several hours or overnight. The layers should be frozen solid.
To remove the cheesecakes from the pans dip the bottom of the pan in a bowl of very hot water, run a knife or spatula around the sides of the cake and flip it out onto a flat plate. Alternately, you can flip the pan over and run a propane torch across the bottom of the pan. Remove the parchment round from the bottom and flip right side up. If not assembling the cake immediately, wrap the cheesecake layers and freeze until ready to use.