Stir curry powder in heavy small skillet over medium-low heat until fragrant, about 2 minutes. Transfer curry powder to small bowl. Stir in mayonnaise and lemon juice. Season with salt and pepper.
Place 1 lavash square on work surface. Spread lavash with 2 tablespoons curried mayonnaise. Place 1/4 of turkey in center of lavash. Top turkey with 1 cup lettuce, 1/2 cup cucumber, 1/4 of mango, and 1/4 of cilantro. Top with 1/4 of avocado slices. Fold in short sides of lavash, then roll up like burrito, enclosing filling completely. Repeat process for remaining 3 wraps. (Can be made 4 hours ahead. Wrap tightly with plastic wrap; keep refrigerated.) Cut wraps in half crosswise.