Recipe adapted from Aran Goyoaga and her blog, Cannelle et Vanille.
In a small saucepan, combine sugar and 1/4 cup water over medium; stir until sugar dissolves. Remove from heat, add mint and lemon thyme, and let sit 10 minutes. Pour through a fine-mesh sieve; discard solids. Refrigerate until cold, 20 minutes (or up to 1 week).
In a blender, combine mint syrup, melon, rum, and lime juice; blend until smooth. To serve, fill four glasses with ice and divide mojito among glasses. Top with fresh mint and lime wedges, if desired.