Preheat oven to 450 degrees F (230 degrees C).
Pour 2 tablespoons of vegetable oil into a large bowl; toss the potato slices in the oil to coat.
Arrange the slices in a single layer on a baking sheet and sprinkle with salt and black pepper.
Bake in the preheated oven until the potato slices are golden brown, about 20 minutes.
While potato slices are baking, heat 1 tablespoon of vegetable oil in a skillet over medium heat; brown the ground beef in the hot oil, breaking it up into crumbles as it cooks, 8 to 10 minutes. Drain excess grease.
Mix the black beans into the ground beef; stir in the taco seasoning and water. Bring the mixture to a boil and reduce heat to medium-low. Simmer until the flavors have blended, about 10 minutes.
Arrange the potato slices on a serving platter and sprinkle with half the Cheddar cheese.
Top the potatoes with the meat and bean mixture; sprinkle the remaining cheese on the nachos.
Spread the lettuce out over the nachos and garnish with tomato and dollops of sour cream and guacamole.
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