In a medium bowl, toss the chicken cubes with lemon pepper seasoning and salt until evenly coated.
In a separate small bowl, whisk together the mayonnaise, chopped capers, minced pickles, 1 teaspoon lemon juice, dried dill, and Dijon mustard. Refrigerate the tartar sauce until ready to serve.
Heat the olive oil in a large non-stick skillet over medium-high heat until shimmering.
Add the chicken cubes to the skillet in a single layer, ensuring they are not overcrowded to prevent steaming.
Sauté the chicken for 3 to 4 minutes per side without moving frequently, allowing a golden-brown crust to form. Cook until the internal temperature reaches 165°F (74°C).
Drizzle the remaining 1 tablespoon of fresh lemon juice over the cooked chicken and toss once to deglaze the pan slightly.
Remove the chicken from the heat and serve immediately with the chilled tartar sauce as a dipping accompaniment.