Add the raspberries, lemon juice, and sugar to a saucepan. Bring to a boil over medium-low heat, stirring regularly, then lower heat and let simmer for 5 minutes. Remove from heat to strain and let cool.
In a food processor, pulse together the shortbread crumbs, a quarter of the white chocolate chips, and the butter. Press into the bottom of jumbo muffin cups and refrigerate while preparing the rest. This will help the crust set.
Beat the cream cheese until fluffy, then add the powdered sugar and beat until smooth. Melt the white chocolate, then add it as well, beating to thoroughly incorporate.
Pour the strained raspberry into the cream cheese and stir. Spoon this over the refrigerated crusts and decorate with raspberries and white chocolate chips. Refrigerate for another 2 hours, or until the cheesecake has set.