Preheat the oven to 400F. Combine the chicken, eggs, bread crumbs, melted butter, celery, Sriracha sauce, and salt in a large bowl. Form the mixture into 1-inch meatballs.
Heat the vegetable oil in a large oven-proof skillet over medium-high heat. Working in batches, cook the meatballs for 5 to 6 minutes, turning a few times while cooking, until browned on all sides. Transfer the pan to the oven and cook for 10 to 15 minutes, until the meatballs are completely cooked through.
Combine the blue cheese, sour cream, buttermilk, and lemon juice in the bowl of a food processor and blend until well combined. Season with salt and pepper, to taste. Serve alongside the meatballs for dipping.