Line an 8-inch square baking dish with parchment paper or foil, leaving a 2-inch overhang on two sides.
Grease the sides and bottom of the paper with butter or cooking spray.
In a bowl, stir together the melted butter and sugar until the sugar is dissolved.
Stir in the graham cracker crumbs.
Press this mixture into the bottom of the prepared baking dish.
Bake until the edges are lightly browned, which usually takes 5 to 8 minutes.
Transfer the crust to a wire rack and let it cool for about 30 minutes.
While the crust is cooling, stir together the sweetened condensed milk, white chocolate chips, and chopped white chocolate in a large saucepan over medium heat until the chocolate is fully melted.
Remove the pan from the heat and stir in the lime zest and juice.
Pour this mixture over the cooled crust, cover it with plastic wrap, and chill it for at least 2 hours, or overnight.
Lift the fudge from the dish using the parchment paper overhangs, then cut it into 1×2-inch pieces.
The fudge can be stored in an airtight container in the refrigerator and will keep for up to 1 week.
