Cook the udon noodles according to package directions until al dente. Drain and set aside.
In a medium bowl, whisk together the soy sauce, chili paste, rice vinegar, lemon juice, honey, toasted sesame oil, chopped garlic, chopped ginger, and 1/4 cup water until well combined.
Heat 1 tablespoon cooking oil in a large skillet or wok over medium-high heat. Add the chicken and season with black pepper. Cook for 5-7 minutes, stirring occasionally, until the chicken is cooked through and lightly browned.
Pour the prepared sauce mixture into the skillet with the chicken. Bring to a low simmer and cook for 2-3 minutes, allowing the sauce to thicken slightly.
Add the cooked udon noodles to the skillet. Toss everything together gently until the noodles and chicken are thoroughly coated with the sticky sauce.
Serve the Honey Garlic Chicken Udon Noodles warm, garnished with sesame seeds. Enjoy immediately!