Add the broth, rice, enchilada sauce, 3/4 teaspoon salt and a couple grinds of black pepper to a rice cooker and stir to combine. Follow the manufacturer's instructions and cook until most of the liquid is absorbed and the rice is tender (a little of the enchilada sauce might pool on the top of the rice, which is okay). Use a rubber or wooden spatula to stir the rice. If the bottom of the rice has browned a bit, stir it into the rest of the rice. Keep the rice warm in the cooker until ready to serve.
Meanwhile, heat the oil in a large straight-sided skillet over medium-high heat. When the oil starts to shimmer, add the beef and let sit for 30 seconds without breaking up. Flip and let sit for another 30 seconds, then break up the meat using the back of a wooden spoon or spatula. Sprinkle liberally with salt. Add the cumin and chili powder and cook, stirring occasionally, until cooked through, about 8 minutes. Add the salsa and cook until warmed through and combined, about 1 minute. Remove from the heat and cover with a lid to keep warm.
When you are ready to serve, stir the lime zest, half of the lime juice and a third of the cilantro into the rice. Taste and season with salt, pepper and the remaining lime juice, if needed. Transfer to a bowl.
Turn on the heat of a gas stove to medium-high. Working with 1 tortilla at a time, use a long pair of kitchen tongs to hold a tortilla over the open flame, turning the tortilla as needed to ensure even toasting, until lightly puffed and toasted in spots, about 30 seconds total. You do not want the tortillas to be crispy, but they should be charred in spots and pliable. Alternatively, you can toast the tortillas under the broiler until toasted in spots. Transfer the hot tortillas to a large platter.
To serve, arrange the lettuce, cheese, sour cream, avocado, lime wedges, remaining cilantro and salsa in bowls and serve alongside the beef, Spanish rice and tortillas.