Rinse the trout under cold water (including the cavity) and pat it dry with paper towels. Make three diagonal slits, ½ inch (1 cm) deep on each side of the thickest part of the fish. This helps impart flavors into the flesh during grilling.
Coat the fish with the olive oil and season it with the salt and pepper. Add the mayonnaise, lemon slices, parsley and dill to the cavity of the fish. The mayonnaise will help keep the flesh succulent throughout the smoking process.
To make the Creamy Dill Sauce, in a small bowl, mix the Greek yogurt, sour cream, horseradish cream, dill, chives, salt and pepper. Refrigerate until needed.
For the Tomato Relish, in another small bowl, mix the sugar and lemon juice until slightly dissolved. Then add the tomato, onion, mint, salt and pepper. Refrigerate until needed.
Prepare a smoker grill for indirect heat and set it to 350°F (180°C. If you’re using a gas grill, add a smoker box filled with pre-smoked apple chips. For a kettle grill, add a handful of apple chips directly to the lit charcoal.
Place the fish on the grill grate in the smoker and cook for 10 minutes a side, or until the fish is cooked through. The fish should flake easily and without resistance away from the bone with a fork when it’s ready. The internal temperature should be approximately 145°F (65°C).
Serve immediately with the Creamy Dill Sauce and Tomato Relish on the side.