In a shallow pan or dish, combine lemon juice, olive oil, chopped onion, paprika, cumin, salt, and bay leaves to create the marinade.
Add swordfish steaks to the marinade, ensuring both sides are well coated.
Cover the dish and refrigerate for 4-6 hours, turning the fish 2-3 times during marinating.
Preheat grill to medium-high heat and lightly oil the grates.
Remove swordfish from marinade and discard the marinade and bay leaves.
Grill swordfish steaks for 4-5 minutes per side, or until internal temperature reaches 145°F and fish flakes easily with a fork.
Remove from grill and let rest for 2-3 minutes before serving.