Trim the ends of the broccolini stalks. If the stems are thick, slice the stalks in half lengthwise. In a high-sided pan with a lid, heat the oil over medium heat. When very hot, add the garlic and cook until soft. Add the broccolini and cook, stirring, until coated in oil, about 2 minutes. Add 1/4 cup water to the pan, turn the heat down to low, cover with the lid, and let simmer for 10 minutes.
Remove the lid, turn up heat and add the zest and lemon juice. Sauté until the water has evaporated. Sprinkle with salt and pepper and serve.