If using raw sugar, bring the water and sugar to a boil in a small pot. Stir the mixture until the sugar is dissolved and then turn off the heat.
Add the torn mint leaves and stir the pot. Allow the simple syrup to cool.
In the meantime, add strawberries to a blender. Place a strainer over the mouth of the blender and pour the mint syrup into the blender (discard the mint leaves).
Add fresh lemon juice into the blender (note: if all the liquid does not fit in the blender, add as much mint/sugar water as you can and add the rest after blending.
Blend on low speed for a few seconds at a time, just enough to break the berries apart but not enough to puree them.
Fill a pitcher with ice, add the mint springs, and pour the lemonade and strawberry mixture over the ice.
Stir and add more ice if necessary.
Notes
The variability of water and lemon juice above depends on how sweet and tart you like your strawberry lemonade. If you are uncertain, you can always start off low, and add more water and lemon juice after blending all the ingredients together.