To make the meatballs, soak breadcrumbs in milk for 10 minutes. When ready, combine bread with turkey, dill, feta, and garlic, and mix gently with hands. Season with salt and pepper; mix just to incorporate. With damp hands, form mixture into small balls (about 1 tablespoon each).
Bring a large pot of salted water to a boil, and add the pasta. Cook, stirring occasionally, until pasta is almost cooked through. Add chard to the pot and finish cooking together, until pasta is al dente.
While pasta is cooking, heat oil in a large, straight-sided skillet over medium-high heat. Add meatballs and brown on all sides, about 2 to 3 minutes. Add stock and bring to a simmer. Cover skillet until meatballs are cooked through, about 5 minutes more. Stir in lemon juice to taste.
Drain pasta and chard together; toss with some liquid from the meatballs.
Transfer to serving bowls, and spoon extra liquid around pasta. Top with meatballs; garnish with dill. Serve immediately.