In a food processor, pulse the avocado and yogurt until smooth. Transfer to a small bowl, fold in the lime juice and refrigerate.
In a large stockpot over high heat, combine the water, celery, onion, carrots, lemons, ginger, lemongrass stalks, wine, sea salt and peppercorns. Bring to a boil, then reduce heat to a low simmer and add chicken breasts. Cover and cook for 15 to 17 minutes. Remove the chicken from the liquid and let rest on a cutting board for 5 minutes. While the chicken is resting, heat the grapeseed oil in a medium saucepan over medium heat. Add the red onion and cook until soft. Reduce the heat and add the black beans, tomatoes, green onion, parsley, and vinegar. Season with salt and pepper, to taste. Stir occasionally, allowing the flavors to blend and the beans to warm, about 4 to 5 minutes. Remove from the heat, and spoon the mixture onto a platter. Slice the chicken and serve on top of the beans with a drizzle of avocado yogurt.