Saute the chicken breast in a hot saute pan with olive oil until golden brown on both sides. Turn down the temperature, put a lid on the pan and cook until the chicken is no longer pink in the center. Remove the chicken from the pan and set aside. Cut the mushrooms and onions into small pieces. Drain off any of the chicken juices from the pan. Saute the onions first in the olive oil, until just about tender. Add the mushrooms and continue to saute until soft and shrunk in size. Season the onions and mushrooms with salt and pepper.
In a small bowl, combine all of the sauce ingredients together while the mushrooms and onions are cooking. Whisk until smooth.
On a cutting board, chop the chicken breasts into small pieces with a knife, or put in a food processor to chop until pieces about the size of a pea. Add the chicken to the mushroom/onion mixture and bring heat back up to medium heat. Add the sauce and let the sauce simmer until it reduces in half. When sauce is thick and items are incorporated, peel and dice the cucumber and stir into the mixture.
Remove from the heat. Wash and rinse the lettuce and serve the chicken mixture into each piece of lettuce. Garnish with green onions if you wish.