In a large bowl, whisk together honey, soy sauce, garlic, lemon juice, olive oil, and sesame oil.
Add the chicken cubes to the marinade and toss until evenly coated.
Cover and refrigerate for at least 1 hour, or up to overnight for deeper flavor.
Soak wooden skewers in water for 30 minutes if using bamboo skewers.
Remove the chicken from the marinade and thread the pieces onto the skewers.
Pour the remaining marinade into a small saucepan.
Mix the cornstarch and water together, then add to the saucepan.
Bring the marinade to a gentle simmer and cook until it thickens into a glaze.
Preheat the grill to medium-high heat and lightly oil the grates.
Place the skewers on the grill and cook for about 10 to 12 minutes, turning frequently.
Brush the skewers with the honey garlic glaze during the final few minutes of grilling.
Continue grilling until the chicken reaches an internal temperature of 165°F (74°C) and develops a caramelized exterior.
Remove from the grill and garnish with sesame seeds, green onions, and lemon wedges before serving.