Place pork on large piece of plastic wrap. Rub tenderloin with oil; sprinkle oregano and lemon pepper evenly over surface. Wrap tightly in the plastic wrap; refrigerate for 2 hours or overnight.
Prepare a medium-hot fire in grill. Unwrap pork. Make lengthwise cut through center of tenderloin. Cut to, but not through, opposite side. Open meat so it lies flat. Spread olive tapénade on half of tenderloin. Sprinkle with cheese. Fold other half of meat over to form original shape of tenderloin. Tie close with twine at 1 1/2 to 2-inch intervals.
Grill tenderloin, uncovered, over direct heat for 20 minutes or until internal temperature reaches 145 degrees F.*, turning tenderloin over halfway during grilling. Transfer tenderloin to cutting board. Loosely cover with foil; let rest for 5-10 minutes. To serve, remove string and cut into 1/4-inch-thick slices.
