Prepare the smoker for barbecuing, bringing the temperature to 200-220°. In a cast-iron skillet or smokeproof baking dish, melt the butter. Stir in the sweet potatoes and then pat the potatoes down into a thick, even layer. Sprinkle the brown sugar and the salt over the potatoes.
Transfer the potatoes to the smoker and cook for 1 hour. Stir in 3 tablespoons of the tequila and half of the lime juice, pat the potatoes back down again and continue cooking the potatoes another 50 to 60 minutes, until they are quite tender but crisped a bit around the edges. Remove the potatoes from the smoker and stir in the remaining tequila and lime juice. Serve warm.