Whisk dressing ingredients together in a salad bowl.
Rub meat with salt and pepper, and drizzle with oil. Preheat a cast-iron skillet over medium-high heat. Grill steak to medium rare, about 8 minutes, remove and let rest. Caramelize the lime halves cut-side down in skillet, 2 minutes.
Thinly slice meat. Douse the meat with juice of caramelized lime.
Add salad ingredients to the bowl with the dressing and toss. Transfer to platter or plates and top with sliced steak.