Combine first 4 ingredients in a large zip-top plastic bag; add mushrooms to bag. Seal and marinate at room temperature for 2 hours, turning bag occasionally. Remove mushrooms from bag; discard marinade.
Prepare grill to medium heat.
Cut bell pepper in half lengthwise; discard seeds and membranes. Place pepper halves on grill rack coated with cooking spray; grill 15 minutes or until blackened, turning occasionally. Place in a zip-top plastic bag; seal. Let stand 10 minutes. Peel. Reserve 1 pepper half for another use. Finely chop 1 pepper half; place in a small bowl. Add mayonnaise, 1/2 teaspoon oil, and ground red pepper; stir well.
Place mushrooms, gill sides down, on grill rack coated with cooking spray; grill 4 minutes on each side. Place buns, cut sides down, on grill rack coated with cooking spray; grill 30 seconds on each side or until toasted. Spread 2 tablespoons mayonnaise mixture on top half of each bun. Place 1 mushroom on bottom half of each bun. Top each mushroom with 1 tomato slice and 1 lettuce leaf; cover with top halves of buns.