Preheat grill to medium-high.
Combine lemon juice, oil, mayonnaise, garlic and pepper in a large bowl.
Oil the grill rack. Sprinkle chicken with salt. Cut romaine in half lengthwise, leaving root ends intact. Grill the chicken, 4 to 6 minutes per side. Two minutes before the chicken is done, place the romaine on the rack and grill, turning once or twice, until lightly charred and beginning to wilt, 2 to 3 minutes total. Cut the chicken into bite-size pieces.
Cut the root ends off the romaine, then chop the leaves. Add the chicken, lettuce and Parmesan to the bowl with the dressing; toss until well combined. Fill each wrap with about 1 1/2 cups of the salad and roll closed.