Add tahini, lemon juice, and salt to food processor and blend. While blending add olive oil and process until smooth.
Remove large leaves off of lettuce head. Slice a thin piece off of the base of the head, careful to keep lettuce head in tact. Cut off a couple of inches off of the top of lettuce. Keep discarded leaves and tops for another salad.
Mix in a small bowl the tablespoon of olive oil, oregano, pepper, and salt. Brush outside of lettuce with oil mixture, spreading it evenly.
Place on grill on medium to high and grill for 10 minutes, stirring occasionally until outside leaves are slightly charred.
Drizzle with Lemon Tahini Dressing and serve immediately.