Combine the water, lemon juice, spinach, chickpea flour, Italian seasonings, sugar, and salt in a high-speed blender. Blend on high until completely smooth (scrape the sides in case there are any clumps of flour). With the motor running, pour the olive oil through the lid plug and blend until incorporated. The batter should be the consistency of thick cream (it will thicken further as it sits). If it’s too thick, add a splash more water. Let the batter sit at room temperature for 15 minutes.
Heat about 1 teaspoon of olive oil (you can just eyeball it) in a 10-inch non-stick skillet over medium heat. Once the pan is hot, wipe the oil around the pan with a paper towel to coat.
Pour in about a heaping ½ cup of the chickpea batter, and swirl and tilt the pan to form a thin circle with the batter. Cook until small bubbles pop on the surface and the bottom is golden, about 1-2 minutes.
Slide a small offset spatula along the edge of the flatbread to loosen it, then use your fingers to flip it over. Cook until golden on the other side, about 30-60 seconds longer. Slide the flatbread out onto a cooling rack. Continue with the remaining batter, rubbing the skillet with more oil as needed to prevent sticking.
Pile the flatbreads with your favorite fixings, and serve.