Cook sweet onion and garlic cloves in butter in a large pot over medium-high heat until translucent, 4 to 6 minutes.
Stir in zucchini and fresh dill; cook 30 seconds.
Stir in chicken stock, cover, and simmer for 3 minutes.
Stir in rotisserie chicken, gnocchi, and green beans.
Cover and simmer until beans are crisp-tender, 3 to 4 minutes.
Stir in baby spinach and lemon juice.
Simmer until spinach is wilted, 1 to 2 minutes.
Season with kosher salt and black pepper.
Serve topped with fresh dill.