Preheat a grill or grill pan to medium heat.
Season the chicken on all sides with lemon pepper seasoning and salt.
Grill the chicken about 5 minutes per side, until cooked through, then transfer to a cutting board and rest at least 5 minutes.
Chop the rested chicken into about 1/2-inch cubes.
Trim romaine leaves so they are about 3 inches shorter than the tortillas.
Dice the plum tomatoes into 1/2-inch cubes and dice the avocado into 1/2-inch cubes.
Warm tortillas briefly if needed so they are pliable (5–10 seconds in the microwave).
To assemble each wrap: lay a tortilla flat, place romaine leaves side by side down the center, sprinkle about 1/2 ounce alfalfa sprouts, and drizzle roughly 1 1/2 tablespoons Caesar dressing over the lettuce.
Arrange about 1/4 cup chopped chicken down the length of one lettuce leaf, then top with 2 tablespoons diced tomato and 2 tablespoons diced avocado.
Sprinkle about 1 ounce shredded cheddar over the fillings.
Fold the short ends of the tortilla inward, then roll tightly from one long edge to form a sealed cylinder with ends tucked under.
Place the wrap seam-side down and cut in half on a diagonal; repeat for remaining ingredients, then serve or wrap for later.