In a medium saucepan over high heat, whisk together the sugar and 3/4 cup of water. Bring to a boil, stirring frequently until the sugar is dissolved. Reduce heat to medium-low, and simmer about 5 minutes, until a slightly thick syrup has formed. Remove from heat. Stir in the large sprigs of mint, and let stand uncovered until the syrup is completely cool. Pour the syrup through a mesh sieve over a bowl and squeeze the mint to extract as much flavor as possible. Discard the mint.

Place the watermelon in a blender or food processor and puree. Pour into a mixing bowl. Stir in the lemon juice. Stir in enough mint syrup to create a very sweet fruit puree. Fold in the sliced mint, then transfer the puree into ice pop molds, leaving some room at the top for them to expand. Cover and freeze until solid, about 4 hours. Hold the molds under lukewarm running water for a few seconds to unmold them, if needed.