In a small bowl, combine the soy sauce, lime juice, sugar and fish sauce; stir until the sugar dissolves. In another small bowl, stir the garlic, 1-1/2 teaspoons of the oil, and 1-1/2 teaspoons pepper.
Season the beef with salt and pepper. In a 12″ nonstick skillet, heat 1-1/2 teaspoons oil over medium-high heat until shimmering hot. Swirl to coat the skillet. Add half of the beef in a single layer and cook, without stirring, until well browned, 1 to 2 minutes. Using tongs, turn the pieces over and brown on the other side, 1 to 2 minutes more. Transfer to a medium bowl. Add 1-1/2 teaspoons oil to the skillet and repeat with the remaining beef, adding to the bowl with the first batch when done.
Put the remaining 1-1/2 Tablespoons oil in the skillet and heat until shimmering hot. Add the onion and cook, stirring frequently, until it begins to soften, 2 to 3 minutes. Add the garlic, mixture and cook stirring constantly, until fragrant, about 30 seconds. Return the beef and any accumulated juices to the pan and stir to combine. Add the soy sauce mixture and cook, stirring constantly, until the beef and onions are coated and the sauce thickens slightly, 2 to 3 minutes.