Melt the coconut oil in a large skillet over medium-high heat. Add onion, garlic and chicken; cook and stir until onion has softened and chicken is cooked through; season with salt, pepper, oregano and cumin then pour half of the lemon juice over the top. Remove skillet from the heat and allow chicken mixture to cool for 5 minutes.
Meanwhile, prepare salad: In a large bowl, toss together next 4 ingredients (kale through cilantro).
Prepare dressing: In a small bowl, whisk together remaining ingredients (mashed avocados through coconut milk) along with remaining lemon juice; salt and pepper to taste. Pour dressing over the salad; toss. Add chicken mixture; toss again then serve.
*Chicken is easier to chop if partially frozen