Put frozen mixed berries in the slow cooker. Squeeze the 1/2 lemon in the slow cooker. Put the sugar in the slow cooker. Add water to the slow cooker, so the crockpot is 2/3 full.
Set the slow cooker for 2 hours on High and press the "Start" button.
After the fruit punch finishes cooking, try it and see if it's sweet enough for you. If it's not sweet enough, you can add more sugar and stir so the sugar is dissolved.
Let the fruit punch come to room temperature on the counter. Strain the fruit punch (I just use a fine-mesh strainer), pour it into a pitcher and put in the refrigerator.