Whisk flour, baking powder, salt, and sugar in a bowl. Stir in warm water until a soft dough forms.
Cover the dough and rest 15 minutes while you prep the toppings.
Brown ground beef with onion in a large skillet over medium-high heat. Drain any excess fat.
Stir in garlic and taco seasoning; cook 1 minute. Add beans, green chiles, and water; simmer until thick, 5–7 minutes.
Heat vegetable oil in a heavy skillet to about 350°F.
Divide dough into 6 balls. Pat each into a 6–7 inch round, about 1/4 inch thick; poke a small hole in the center.
Fry rounds in hot oil, 60–90 seconds per side, until puffed and deep golden. Drain on a rack or paper towels.
Spoon warm beef-bean mixture over fry bread. Top with lettuce, tomatoes, cheese, sour cream, salsa, and cilantro.
Finish with a splash of lime juice and serve immediately.