Squeeze the lemons. Transfer the lemon juice to a large mixing bowl and set aside.
Add 1 cup of water, 1 ½ tablespoons of sugar, and the blackberries to a medium saucepan. Place over high heat and bring to a boil. Cook for 5 minutes.
Place a strainer over a medium mixing bowl. Pour the blackberry mixture into the strainer. Just the back of a spoon to press out any additional liquid. Pour the syrup into the lemon juice.
Add 1 cup of water and ¾ cup of sugar to a medium saucepan. Place over medium-high heat and bring to a boil. Cook for about 2 minutes until the sugar is completely dissolved. Pour into the blackberry/lemon mixture.
Add 3 cups of ice to a 2.5-quart pitcher. Pour in the blackberry/lemon mixture along with 2 cups of cold water. Stir everything together. Store in the fridge until ready to serve.
Notes
The blackberry syrup and simple syrup can both be made ahead of time. Store in an airtight container in the fridge until you're ready to mix up the lemonade.