Preheat the oven to 350F/180C. Line an 8×8-inch baking pan with parchment paper, leaving enough overhang on the sides for lifting the cheesecake out after baking.
In a medium bowl, stir the crumbs and melted butter together. Put mixture in the lined pan and gently press with your fingers until crumbs form an even layer. Bake for 8 minutes. Allow to cool while you prepare the filling.
Reduce oven temperature to 300F/150C.
In a medium heat-proof bowl, combine the white chocolate and heavy whipping cream. Melt in the microwave in 20 second-intervals, stirring between each interval, until melted. Alternatively, set the mixture over a saucepan of simmering water, stirring occasionally.
In a mixer fitted with the paddle attachment, beat cream cheese on medium speed until smooth, about 1 minute. Add sugar and beat for another 2 minutes. Scrape down the sides and bottom of the bowl as necessary. Add eggs, one at a time, until fully combined. Add vanilla, lemon zest and juice and beat until incorporated and smooth. Stir in the chocolate mixture and mix until combined.
Pour batter over the cooled crust and spread evenly. Sprinkle with chocolate chips if desired. Bake for about 45 minutes. The center of the cake should be slightly wobbly when it’s taken out of the oven. Allow the cake to sit at room temperature for 1 hour, then refrigerate for 4 hours (or, preferably, overnight) until completely set. Lift the cake out of the pan using the parchment paper and cut into squares.