Preheat an electric smoker to 250°F. Set it up according to the manufacturer’s instructions, and use your preferred mild wood chips.
In a large bowl, stir together the egg, breadcrumbs, and milk. Let the mixture sit for 2 minutes so the breadcrumbs can absorb the milk.
Add the ground beef, pepper jack, drained green chiles, onion, cumin, chili powder, salt, and black pepper. Mix gently just until combined. Avoid packing the mixture tightly, which can make the loaf dense.
Shape the mixture into a loaf about 8 inches long. Place it on a small sheet of foil with the edges slightly raised, or on a smoker-safe rack with a drip pan beneath it.
Smoke the meatloaf until the center reaches 160°F on an instant-read thermometer, about 2 to 2½ hours. Check the temperature in the center of the loaf.
Stir the lime juice into the barbecue sauce. Brush half of the mixture over the meatloaf during the last 20 minutes of smoking. Once the loaf reaches 160°F, remove it from the smoker and brush on the remaining sauce.
Let the meatloaf rest for 10 minutes before slicing. This helps the slices hold together and gives the melted cheese time to settle.