Soak whole sprouts in a large bowl of cold, salted water to clean. Then trim and discard ends and any bitter outer leaves. Cut each in half lengthwise, then slice thinly across width.
Melt butter in a large skillet over medium-high heat. Saute sprouts with salt and pepper until they start to brown. Add water and cook until barely limp, about 4 minutes. (The water changes the action from sauteing to steaming.) Stir in lime juice and serve immediately.