In a large frying pan, heat the olive oil over medium heat. Add the garlic and saute until lightly golden, 1 to 2 minutes. Stir in the kale and vegetable stock. Cover, reduce the heat to medium-low, and cook until the kale is wilted and some of the liquid has evaporated, about 5 minutes.
Stir in the tomatoes and cook uncovered until the kale is tender, 5 to 7 minutes longer. Remove from the heat and stir in the lemon juice, salt and pepper. Serve immediately.