Preheat oven to 425 degrees. On a rimmed baking sheet, arrange bread in a single layer and brush with 3 tablespoons oil. Season with salt and pepper and bake until golden, 10 to 12 minutes.
Top crostini with apple and prosciutto. Toss arugula with lemon juice and remaining tablespoon oil, season with salt and pepper, and divide among crostini.