Combine oil, lemon juice, garlic, oregano, salt, and pepper in sealable plastic bag. Add lamb and seal bag, pressing out air. Turn bag to coat lamb, then put bag in a shallow baking pan and marinate, chilled, turning bag over occasionally, at least 8 hours.
Bring lamb to room temperature, about 1 hour, before grilling.
Prepare grill for cooking over direct heat with medium-hot charcoal (moderate heat for gas); see Grilling Procedure.
Remove lamb from marinade (discard marinade) and run 3 or 4 skewers lengthwise through lamb about 2 inches apart. Grill on a lightly oiled grill rack, covered only if using gas grill, turning over occasionally and, if necessary, moving around on grill to avoid flare-ups, until thermometer registers 125 to 128°F, 8 to 14 minutes total for medium-rare.
Transfer lamb to a cutting board and remove skewers. Let lamb stand, loosely covered with foil, 20 minutes. (Internal temperature will rise to 135°F while meat stands.) Cut across the grain into slices.
