Remove center stem from cleaned greens and slice into 1/2 inch ribbons. Pour oil in large Dutch oven over medium high heat. Once it is hot add onions and garlic, sauté until fragrant, 4 minutes. Season with salt and pepper. Add all greens except swiss chard. Add in batches, as one batch wilts down add another until they are all in the pot.
Once all greens are in the pot add the broth and cook for 10 minutes. Then add swiss chard, cover with a lid and let simmer 4-5 more minutes. Taste for seasonings. Squeeze fresh lemon juice over all and serve.