In a wide, shallow container with a lid, add the avocado or vegetable oil, soy sauce, sugar, ginger, garlic and sesame oil. Whisk to combine.
Add the steak and coat in the marinade. Cover and refrigerate for 4 to 6 hours.
Remove the steak from the refrigerator to come to room temperature before cooking, about 1 hour.
Preheat a grill or grill pan to medium-high heat. Remove the steak from the marinade, pat dry and sprinkle with salt and pepper.
Cook for 2 to 3 minutes per side for medium-rare with an internal temperature of 125 degrees F. Remove from the heat and set aside to rest, about 10 minutes.
Squeeze the juice of the lime on the rested steak and slice against the grain.