Heat oven to 400° F.
In a medium bowl, combine the beans, corn, and salsa.
Place 4 tortillas on a parchment- or foil-lined baking sheet. Sprinkle with half the cheese. Using a slotted spoon, transfer the black bean mixture on top of the cheese. Sprinkle with the remaining cheese and sandwich with the remaining tortillas. Bake until the cheese has melted, 5 to 7 minutes.
Meanwhile, in a large bowl, combine the onion, cilantro, salt, pepper, lime juice, and oil. Add the lettuce and toss.
Transfer the quesadillas to a cutting board. Cut each into 6 wedges. Serve with the salad.