Place an oven rack in the center of the oven. Preheat the oven to 170 degrees F or the lowest setting on the oven. Line a rimmed heavy baking sheet with a silicone baking mat.
Place the strawberries, agave and lemon juice in a blender. Blend until smooth. Pour the puree onto the prepared baking sheet. Spread the puree evenly leaving a 1-inch border around the edge of the baking sheet using a spatula.
Bake until the center of the puree has set and is not sticky when touched, 6 to 7 hours.
Cut into 1-inch-wide strips using scissors and roll up between strips of parchment paper.
Alternatively, the baked puree can be cut into shapes using decorative-edged scissors or cookie cutters.