Do Ahead: Dice the watermelon, put it in a bowl, and stick it in the freezer. You can keep frozen diced watermelon in the freezer at all times so you’re ready to make this at any moment’s notice.
Measure 4 cups frozen watermelon cubes and add to the blender with about ¼-½ cup water (if your blender doesn’t hold this, you can make smaller batches). The watermelon themselves have enough liquid for the drink, you just need a bit to get the blender started. Blend until watermelon is smooth. You will need to stop the blender and move the chunks around a couple of times. If you need a bit more water, go ahead.
Add a squeeze of lime and honey at any point.
Once the watermelon is smooth, measure 2 cups of frozen strawberries. Add strawberries to the blender, a few at a time, and blend until smooth.
Repeat with remaining watermelon and strawberries (I had 2 cups watermelon and 1 cup strawberries remaining to blend, the same ratio). Add to cold cups with lids and straws.
If you want to make this ahead, store in the freezer. Remove from freezer about 1 hour before serving.