Heat 2 tablespoons oil in a large pot over medium heat. Add onion; cook and stir until lightly browned, about 7 minutes. Stir in garlic and ginger; cook until fragrant, about 2 minutes. Add curry powder; cook and stir until fragrant, about 1 minute.

Pour vegetable stock and coconut milk into the pot. Add yam, carrots, celery, lentils, lemongrass, and sugar. Increase heat to medium-high; bring to a boil. Reduce heat slightly; simmer until vegetables soften, 10 to 15 minutes. Season soup with salt.

Heat remaining 3 tablespoons oil in a large nonstick skillet over medium heat. Add tofu in a single layer; cook until lightly browned, about 4 minutes per side. Stir tofu into soup.