Preheat oven to 190 C / Gas 5. Line a 20cm square baking tin with baking parchment or foil, leaving a 5cm overhang. Butter sides and bottom of parchment.
Stir butter and sugar together in a bowl until sugar is completely dissolved. Stir biscuit crumbs into butter mixture; press mixture into the bottom of the prepared baking tin.
Bake in the preheated oven until edges are lightly browned, 4 to 5 minutes. Cool completely.
Stir condensed milk, white chocolate chips and white chocolate together in a large saucepan over medium heat until chocolate is completely melted. Remove saucepan from heat and stir lime juice and lime zest into white chocolate. Pour mixture over cooled base, cover with cling film and chill in the fridge for at least two hours or overnight.
Lift fudge from tin using the overhanging paper and cut into desired shapes. Store in a container in the fridge.