Preheat the oven to 450 degrees F (230 degrees C).

Add 2 tablespoons vegetable oil to a large bowl. Add potato slices to the bowl; toss to coat in oil.

Arrange potato slices in a single layer on a baking sheet; sprinkle with salt and black pepper.

Bake in the preheated oven until potato slices are golden brown, about 20 minutes.

Meanwhile, heat remaining 1 tablespoon vegetable oil in a skillet over medium heat; add ground beef. Brown, breaking into crumbles as it cooks, 8 to 10 minutes. Drain excess grease.

Stir black beans into ground beef, then stir in taco seasoning and water. Bring beef-bean mixture to a boil, then reduce heat to medium-low. Simmer until flavors have blended, about 10 minutes.

Arrange potato slices on a serving platter; sprinkle with ½ Cheddar cheese. Top with meat-bean mixture; sprinkle with remaining ½ cheese.

Spread lettuce over nachos; garnish with tomato. Dollop on sour cream and guacamole.