Wash the Limes Well: Seriously well. Soap and water.
Cut the Limes: Slice them into 4 wedges each.
Blend the Limes: Add lime wedges and water to a high speed blender. Blend until mixed well.
Strain the Mixture: Pour through a wire strainer into a clean container. Discard all rind pieces and chunks.
Return Liquid to Blender: Pour strained lime water back into the blender.
Add Remaining Ingredients: Add strawberries, sweetened condensed milk, sugar, and ice.
Blend Again: Blend until smooth and creamy.
Serve Immediately: Stir before serving if needed because it settles quickly.