Bring 6 cups water and pineapple to a boil over high heat; cover, reduce heat to medium-low, and simmer 20 minutes. Remove from heat; stir in basil leaves. Cover and let stand 10 minutes. Add sugar, stirring until dissolved.
Process pineapple mixture and strawberries in a blender, in 3 batches, until smooth. Pour mixture through a fine wire-mesh strainer into a pitcher, discarding solids. Stir in lemon juice. Serve over ice, or cover and chill until ready to serve.