Preheat the oven to 350 degrees F.

Toss the avocado slices with the lime juice in a small mixing bowl. Season with salt and pepper.

Heat the refried beans in a microwave safe bowl until warm, stirring until smooth.

Arrange the bread slices in pairs on a cutting board. Slather each piece of bread with a scant tablespoon of refried beans. Arrange the cheese on half of the of bread, followed by the avocado. Top with the remaining bread, bean-side down.

Heat a large non-stick skillet over a medium flame. Brush the pan with olive oil. Cook the sandwiches in batches until golden brown on both sides, about 2 minutes per side. Remove the grilled cheeses to a baking sheet.

Bake the sandwiches in the oven until the cheese is very melted, about 3 to 5 minutes more.