Combine strawberries, water, agave syrup (starting with 1/2 cup), and lemon juice in a blender. Blend on medium-high speed until completely smooth, about 30 seconds.
Taste the lemonade and adjust the flavor as needed (more agave syrup for sweetness, more lemon juice for acidity, more strawberries for taste).
For a smoother texture, strain the lemonade through a fine mesh strainer (optional but recommend).
Chill the lemonade in the refrigerator for at least 6 hours, or overnight, for best flavor. You can also serve immediately over ice.