Put the lemon juice with 1teaspoon salt in a small bowl. Mix together thoroughly with a small whisk or fork until the salt is dissolved. Chop enough of the oregano leaves to measure 2teaspoons and add it to the bowl. Whisk in the olive oil until emulsified.
Season the swordfish on both sides with salt and pepper and place it on the grill. Cook for 2 to 3 minutes on each side until barely pink in the center. Transfer to a serving platter, pour the sauce over it, and serve at once.