Soak dried porcini in 1 cup hot water for 30 minutes.
Roll the lemon on a hard, flat surface, pressing with your palm, to help release the juices inside. Cut the lemon in half.
Remove the skin from the chicken pieces and rub the cut side of the lemon, squeezing gently, over the meat (use both halves to use all the lemon juice).
Heat oil in a pan large enough to hold the chicken pieces in one layer. Add the prepared chicken and brown on both sides. Transfer to a casserole dish.
Preheat oven to 350 degrees F.
In a pan over medium heat, melt the butter. When it stops foaming, add chopped onion and salt, then sauté until pale gold.
Meanwhile, remove the porcini from the water and rinse well. Pat the porcini dry and chop into small pieces. Strain the water through a sieve, stopping before the last spoonful so that you don’t get the residue from the bottom.
Add porcini and pumpkin pieces to onion and sauté for 5 minutes. Add fresh mushrooms and cook for 5 minutes more, stirring frequently.
Stir in the half and half, 4 to 5 Tbsp of the strained porcini water and season to taste with salt and freshly ground pepper. Simmer uncovered for 10 to 12 minutes until reduced slightly, then pour over the chicken in the casserole dish.
Cover and cook in a 350 degree F oven for 30 to 40 minutes, turning the chicken once or twice and adding a few spoonfuls of water or unsalted chicken broth if the sauce becomes a little dry.