In a large stockpot over high heat, add the water, salt, and honey. Stir to combine, cook just until the honey and salt are fully dissolved. Take off the heat and add the ice cubes. Stir until melted.
If the pot is large enough to hold the chicken, place the whole chicken directly into the pot with the brine. If it is not large enough, transfer the brine to a large container and add the chicken. Cover, and let sit in the refrigerator overnight.
Before smoking, prepare your smoker per the manufacturer's instructions and preheat to 225°F. Take the chicken out of the brine and pat dry with paper towels.
Sprinkle the rub all over the outside of the chicken and rub it into the skin. Stuff the cavity with the lemon, garlic, onions, and thyme. Tie the legs together with twine and place directly onto the grill of the smoker.
Close the lid and smoke until the internal temperature when checked with a meat thermometer in the thickest part of the breast reaches 160°F. Take the chicken off the smoker and let rest for 15 minutes before carving.