Trim steak and thinly slice against the grain. In a nonreactive mixing bowl, combine the lime juice, 2 tablespoons of the vegetable oil, garlic and sliced steak. Toss to coat well. Cover and refrigerate for at least 2 hours and up to 4.
Preheat the oven to 325 degrees.
Wrap the tortillas in foil and place in the oven until warmed through, about 15 minutes.
Remove from the oven and set aside (covered) until ready to serve.
In a large skillet, heat one tablespoon of the remaining oil over medium-high heat.
Cook one-third of the marinated steak until well browned on both sides, 4 to 6 minutes.
If necessary, remove any excess liquid and wipe pan clean between batches. Repeat, using an additional tablespoon of oil for each remaining portion of steak, until all steak has been browned.
Set browned steak aside and keep warm while you cook the vegetables.
Add the remaining tablespoon of oil to the pan, along with the peppers and onions, and cook, stirring, until soft and slightly caramelized, 10 to 12 minutes. Add the garlic and cook, stirring, until the garlic is fragrant and soft, 1 minute.
Serve the fajitas with the warmed tortillas, sautéed peppers and onions, and condiments of choice. Makes 6 servings.