Mash the raspberries with the mint and sugar in a large bowl, using a potato masher or muddler, until the raspberries break down into very small pieces. Add the rum, lime juice and Lillet and stir to combine. Cover and refrigerate 1 to 4 hours.
Strain the mixture into a large pitcher with ice. Add some raspberries and mint for garnish and top off with the seltzer. Serve immediately.