Bring a large pot of salted water to a boil. Make the brine: Combine the vinegar, half of the lemon juice, 1/2 cup water, the sugar, coriander, 1 teaspoon salt and a pinch of pepper in a saucepan. Bring to a boil and cook 1 to 2 minutes. Put the bell pepper and red onion in a bowl; pour in the brine. Let cool to room temperature.
Cook the green and wax beans in the boiling water until crisp-tender, 3 to 4 minutes. Drain and rinse. Transfer to a large bowl along with the black beans.
Reserve 1/4 cup brine, then drain the bell pepper and onion and add to the beans. Make the vinaigrette: Whisk the reserved brine, the remaining lemon juice and the mustard in a bowl, then whisk in the olive oil until smooth. Toss with the bean mixture. Cover and refrigerate at least 1 hour. Stir in the cilantro and season with salt and pepper before serving.