In a small bowl, mix the stevia and xanthan gum together and set aside.
Pour the agave, lemon juice, and water into a high-powered blender. Cover the blender and blend until the ingredients are well combined. Add the stevia and xanthan mixture to the blender. Cover the blender again and blend the ingredients on low until the mixture is well combined, about 10 seconds. Turn off the blender.
Add the still-frozen strawberries to the blender. Cover and blend on high while pushing the strawberries down into the blade with the wand until the mixture is smooth but still frozen, about 5 to 10 seconds.
Spoon the strawberry ice into paper cups or chilled bowls and serve it immediately. This ice will stay fresh and tasty, tightly covered, in the freezer for up to a month. If it is too hard after freezing, simply temper in the refrigerator for 30 minutes before serving or put in the microwave on high for 5 to 10 seconds until just soft enough to scoop.