If using fresh watermelon, slice it into cubes and place them in a blender. Pulse until smooth. Strain out the solids with a fine-mesh strainer. Use a spatula to push the liquid through the mesh. Repeat the straining process to remove even more sediment.
Then, make a simple syrup on the stove with which to sweeten the lemonade. Heat 1 cup water and sugar on the stove over medium heat. Stir until sugar dissolves, then remove from heat and let cool slightly.
Combine the lemon juice, simple syrup and watermelon juice in a pitcher. Top with remaining 5 cups cold water. Refrigerate until ready to drink.
Notes
I juiced a 2 pound watermelon: It made 4 cups of juice. Tips
Use the juice from fresh lemons. When making lemonade, where lemon juice is the star, it makes a big difference in flavor.
Be sure to use room-temperature citrus. Refrigerated lemons will not juice as well as ones that have been warmed up.You can microwave them briefly for about 10 seconds to get a to warm them up or just leave them out for an hour or two before you plan to juice them.
Sweeten it to taste, add a little bit of syrup and add more as desired.
Settling is normal. Stir or shake the lemonade up if you notice some watermelon pulp has sunk to the bottom.