Heat oil in a large frying pan until hot. Season the chicken all over with salt and pepper, then fry until golden brown, about 5 minutes on each sides
Add the thyme, garlic, butter, and water to the pan. Reduce the heat to medium- low, partially cover the pan, and braise until the chicken is tender, 30 to 35 minutes. Turn the chicken halfway through the cooking. The chicken is done when nice and tender and the juice reduced by half.
About half way into cooking the chicken, 15 minutes, melt the remaining 2 tablespoons of butter in another pan and add the onions. Toss well and cook over medium to low heat, stirring frequently, until the onions are tender, 8 to 10 minutes. Add the thyme springs, peas and water. Season well.
Simmer until the peas and most of the water has evaporated, 5 to 6 minutes. Add the lettuce and stir until just wilted, about 2 minute longer. Serve the chicken over a bed of peas and onions.
Giangi's Kitchen provides nutritional information, but these figures should be considered estimates, as a registered dietician does not calculate them.