Mix 3 cups water and lemon juice in a large pitcher. Refrigerate until chilled.
Bring remaining 3 cups water, sugar, lavender, and hibiscus petals to a boil in a saucepan. Reduce heat to medium-low and simmer for 10 minutes. Remove from heat and allow to cool. Strain lavender and hibiscus from liquid and pour into pitcher with lemon water. Refrigerate until cold.