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.
To serve as individual drinks, prepare the punch without the seltzer and divide between 6 or 8 glasses with ice. Top each glass with seltzer and serve immediately