Roughly quarter the lemons and limes.

Place the citrus quarters in a blender.

Add 4 cups of the cold water to the blender with the citrus.

Blend on high for about 30-60 seconds, or until the citrus peels are mostly pulverized. Be careful not to over-blend, as this can make the drink bitter.

Immediately pour the blended mixture through a fine-mesh sieve (or a nut milk bag/cheesecloth-lined colander) into a large pitcher or bowl. Use the back of a spoon to press out as much liquid as possible, discarding the pulp and seeds. This step is crucial for removing bitterness.

Rinse the blender.

Add the hulled strawberries, fresh basil leaves, and the remaining 2 cups of cold water to the blender.

Blend until the strawberries and basil are completely pureed and the mixture is smooth.

Pour the strawberry-basil puree into the pitcher with the strained lemon-lime base.

Add the entire can of sweetened condensed milk to the pitcher.

Stir vigorously until everything is thoroughly combined and the condensed milk is fully dissolved.

Taste the lemon limeade and adjust sweetness or tartness if desired (you can add a bit more condensed milk for sweetness, or a squeeze more fresh lemon/lime juice for tartness).

Refrigerate for at least 30 minutes to chill completely.

Serve over plenty of ice, garnished with extra strawberry slices, fresh basil sprigs, or citrus slices.