Combine the sugar with the lemon zest, lemon juice, lemon paste and water in a small saucepan. Warm over medium heat until the sugar is completely dissolved, stirring occasionally, about 5 to 7 minutes. Set aside to cool.
Place about half of the watermelon in a blender and process on medium-low, until liquefied, using the tamper as needed. Add the remaining watermelon and process on medium speed until very smooth, about 1 to 2 minutes.
Strain the watermelon purée through a wide sieve into a large container. Measure out 3 cups of watermelon purée for the sorbet.
Add the raspberries along with ½ cup of the watermelon purée (measured out for the sorbet) into the canister of the blender. Process on medium speed until very smooth, about 1 to 2 minutes, adding more watermelon purée if needed to blend.
Strain the raspberries through the sieve and add to the reserved watermelon purée.
Stir the lemon simple syrup into the watermelon and raspberry purée. Cover and refrigerate until chilled.
When you’re ready to churn, stir the sorbet mixture – it will separate slightly as it chills. Pour it slowly into an ice cream maker and churn until the mixture is partially frozen. Don't over churn or the sorbet will be icy in texture. Transfer to a freezer-proof container and freeze until the sorbet is set.