For the watermelon ice cubes: In a blender, puree the watermelon with the Simple Syrup and lime juice. Pour into a silicone ice cube tray and freeze about 8 hours.
For the shandy: When the ice cubes are ready, cut a slight slice off the bottom of the watermelon so it sits upright. Carefully cut across the top quarter of the watermelon, leaving three-quarters left. Scoop out the watermelon with an ice cream scoop, reserving the insides for another use (or use to make the watermelon ice cubes). Cut a V-shaped notch in one side of the watermelon.
Put 4 watermelon ice cubes in the hollowed-out melon. Pour in the lemonade until it fills it about three-quarters full. Quickly immerse the beer bottle into the lemonade, leaning it in the notch and making sure the opening of the bottle hits the watermelon floor.
Combine the sugar and 1 cup water in a small saucepan and bring to a boil. Cook, stirring, until the sugar dissolves. Remove from the heat and let cool completely. Keep covered in the refrigerator up to 1 month.