Place trout, 1 onion, beer, and lemon in a heavy bottomed pot. Bring to a boil; reduce heat to medium and cook until trout easily flakes with a fork, about 15 minutes. Transfer trout to a flat work surface and remove skin. Discard beer, onion, and lemon.
Place salt pork in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 5 minutes. Reserve drippings and drain salt pork on paper towels.
Melt butter in the skillet. Add remaining onion and celery; saute until almost tender, about 5 minutes. Transfer to the pot. Stir in chicken stock, potatoes, salt, and pepper. Bring to a boil. Reduce heat to medium-low and simmer until potatoes are tender, about 20 minutes.
Place trout, salt pork, and heavy cream into the pot. Cook until chowder is heated through, about 5 minutes. Garnish with parsley and chives.