Combine soy sauce, teriyaki sauce, honey, lemon juice, garlic, black pepper, and ginger in a large resealable plastic bag. Add Cornish hens. Seal and marinate in the refrigerator for 8 hours.
Preheat oven to 400 degrees F (200 degrees C). Grease a metal rack and set inside a roasting pan.
Transfer hens from the plastic bag to a flat work surface; tie legs together with kitchen twine. Place hens on the prepared rack.
Pour marinade into a small saucepan; bring to a boil. Remove from heat.
Roast hens in the preheated oven, basting occasionally with marinade, until juices run clear, about 1 hour. Cover loosely with aluminum foil. Continue roasting until an instant-read thermometer inserted into the thickest part of the thigh, near the bone, reads 165 degrees F (74 degrees C), about 15 minute more.
Cover hens with aluminum foil. Let rest for 5 minutes before serving.