Heat oil in a large skillet or saucepan and brown pork, in batches, until golden. Transfer browned pork to a bowl. Discard fat and return pork to skillet with onion, celery, bay leaf, stock and water.Cook over low heat, uncovered for 1 ½ hour, until pork is tender. Add carrots, cover pan and continue cooking, over low heat until tender. Remove pork and carrots to a bowl and strain liquid. Return liquid to pan and bring to a boil until reduced to 3 cups. Reserve.
Melt butter and sauté mushrooms stirring occasionally until most of the liquid the mushrooms give off, is evaporated. Sprinkle flour and cook stirring. Add heavy cream and stir. Add mushroom mixture to reserved cooking liquid. Cook over low heat, stirring until thickened. Add lemon juice, pork, carrots, salt and pepper. Stir in parsley and serve with rice.