Combine the yeast, sugar, and 1/4 cup warm water in a food processor and pulse to blend. Cover and let stand until bubbly - about 5 minutes.
Add the flour and salt and pulse again to combine. With the machine still running add the 11/8 cups warm water and the olive oil and continue to process until a soft, tacky dough forms - about 20 seconds.
Turn the dough out onto a lightly floured surface and knead by hand for 1 to 2 minutes. Form it into a ball and put into a deep bowl, lightly brush with oil, cover the bowl with plastic, leave in a warm place, and let the dough rise until doubled in bulk - about 2 hours.
Turn the risen dough back onto a lightly floured surface and knead again for 1 minute. Split the dough into 2 even balls.
Sprinkle salt over the spinach, and over the onions in separate colanders or strainers, and let stand for at least an hour. Rinse the salt off very well or it will end up too salty. Immerse the spinach, and the onions separately, in several changes of water. Squeeze as much of the water out as possible when done.
Heat oil in a pan and sauté onions for 2 minutes (do not brown them). Add the lemon juice and cook until it's evaporated. Add spinach and stir constantly for another 2 minutes. (If it's young, tender spinach you can skip the 2 minutes of cooking.) Add the remaining ingredients. The object of all this cooking is to soften the onions, and evaporate the juice off of everything else. Filling must be dry at the end of cooking or it will mess up the dough.
Take half of the dough (which is half of what you made in the recipe above). Divide it into four parts, then divide each of these into 4 parts (1/16ths of the half of the dough you started with.) Flatten each little ball of dough and let rest for 10 minutes. Roll it out into a thin, 5-inch round. Place approximately 2 Tablespoons of filling in the center of the round, fold in half, brush the edge with a little water and pinch it shut. You can also squish the edges shut with a fork for an aesthetically pleasing look.
Bake at 400° for 20-30 minutes, until golden brown.