Heat the sugar and water over medium heat, stirring often, in a small saucepan until the sugar has completely dissolved to make a simple syrup.

Puree the raspberries in a blender or food processor and pour in the simple syrup and lemon juice.

Add extra water (or Sprite, if you want it fizzy - but it won't be like Cheesecake Factory's recipe) to thin it out to the consistency and flavor that you like.

Run a lemon slice around the rim of your glass, dip the glass in sugar, and serve with ice.