Bring a large pot of water to boil. Chop kale into 1-in. pieces and add to pot. Cover and cook until slightly wilted, 3 to 5 minutes. Drain.
In a large frying pan or heavy-bottomed pot, cook garlic in olive oil over low heat, stirring often, until soft, about 3 minutes. Add kale and wine and cook, covered, until almost dry. Add chicken stock and cook, covered, until stock is almost evaporated and kale is very tender, about 30 minutes (if kale isn't tender, add more stock and continue cooking). Season to taste with salt and lemon juice.
Note: Nutritional analysis is per 1/2-cup serving.