Whisk soy sauce, brown sugar, sesame oil, green onions, lemon juice, sesame seeds, ginger, and garlic together in a bowl until marinade is smooth.
Thinly slice steak with the grain into 1/4-inch thick pieces. Thread steak slices onto skewers and place in a flat plastic or glass container. Pour marinade over skewers. Cover container with plastic wrap, and refrigerate, 1 1/2 to 2 hours. Flip skewers and continue marinating in the refrigerator, 1 1/2 to 2 hours more.
Preheat an outdoor grill for high heat, and lightly oil the grate. Remove skewers from marinade, discarding marinade.
Cook steak skewers on the preheated grill until cooked through, 2 to 3 minutes per side.