In a 1-gallon pitcher, add 4 cups of ice and set aside. In a medium saucepan, bring 2 cups of water to a boil. Add the blueberries, sugar and lavender to the pan. Boil for about 5 minutes, until the blueberries have popped and all of the sugar has dissolved.
Strain the blueberry mixture over the pitcher of ice; discard the remaining blueberry mixture. Add the lemon juice and Splenda to the pitcher. Fill to the top with cold water. Mix well.