Mix graham cracker crumbs, sugar and melted butter until well blended. Line 12 cupcake cups with the foil liners. Press graham cracker mixture to the bottom of each foil liner. Reserve remaining crumbs for garnish.
Place the cream cheese in a large mixing bowl. With an electric mixer on low speed, beat the cream cheese until creamy, 30 seconds. Turn off the machine and add the sweetened condensed milk and Key lime juice. With the mixer on medium speed, blend until just combined, 20 to 30 seconds. Stop the mixer, add 1 cup of the whipped topping, and blend on low speed to combine, 15 seconds.
Spoon the lime mixture on top of the crusts in the foil liners. The liners should be very full, but not overflowing. Cover the pan with plastic wrap and place in the freezer until firm, at least 3 hours.
To make the lime twists, cut the large lime into 12 very thin slices. Cut each slice halfway through from the edge to the center, then twist the lime into a spiral with your fingers.
Remove the pans from the freezer about 15 minutes before serving. To serve, peel away the foil liners and place the cakes on serving plates. Dollop with 1 heaping tablespoon of the remaining whipped topping. Sprinkle with the reserved cookie crumbs and garnish with a lime twist. (You can store these cupcakes, covered with plastic wrap, in the freezer for up to 2 weeks.)