Season the beef with salt and pepper. In a medium bowl, whisk together the lime juice, soy sauce, sugar, garlic and chile until the sugar is dissolved. Add the beef, toss to coat and set aside.
In a large skillet over medium-high heat, heat the oil until shimmering, about 1 minute. Then add the beef and cook, stirring, until cooked through, 3 to 5 minutes.
Remove the beef from the skillet and set aside. Allow the liquid in the skillet to reduce until thickened, about 4 minutes. Add the mushrooms, spring onions and asparagus and cook until all the vegetables are tender-crisp, 5 to 7 minutes. Return the beef to the skillet and toss to combine.