Remove stems from shiitake mushrooms; discard or save for stock. Thinly slice shiitake caps; quarter button or cremini mushrooms. Toss together. (mushrooms can be prepared ahead, covered and chilled for up to a day).
Heat 1 T butter in a large frying pan over medium heat until hot and bubbly. Add half of the mushrooms and 1 T lemon juice. Saute 3 minutes, turning frequently or until lightly browned and almost cooked. Turn into a bowl. Again with more butter and juice, saute remaining mushrooms in the same manner; turn into bowl.
Reduce heat to medium.
Drain juices from bowl into pan; add shallot and garlic. Cook 2 minutes or until softened. Meanwhile stir in flour, salt and pepper into 1/2 cup cream; pour into shallot mixture. Bring to a boil, stirring constantly; bubble 1 minute.
Return mushrooms to pan. Cook, stirring frequently, for 5 minutes or until hot, bubbling and sauce has thickened. Turn into warmed serving dish. Sprinkle with parsley and drizzle with remaining 2 T cream.