Place the salmon in a zip-top bag. Mix the soy sauce, orange juice, garlic, mustard, tomato paste, and lemon juice in a bowl. Pour into the bag with the salmon.
Seal the bag, pressing out excess air.
Refrigerate to marinate 4 to 6 hours.
Prepare a grill. Remove the salmon from the bag, reserving the marinade.
Place the salmon on the grill and cook, turning once, for about 5 minutes on each side, or longer for well done.
For extra flavor, lightly drizzle a few tablespoons of the marinade on salmon during grilling. Discard leftover marinade.