Coat the bottom of a slow cooker crock with olive oil. Put celery, carrots, potato, onion, lettuce, beer, shallots, fennel, bell pepper, apple, parsley, peppercorns, lemon, ginger, tamari, Worcestershire sauce, garlic, and bay leaf into the slow cooker crock. Pour water over the ingredients.
Cook on Low for 8 to 10 hours, or on High for 4 hours.
Remove and discard all solid chunks from the liquid using a slotted spoon.
Line a colander with cheesecloth and set over a large pot; strain broth through the cheesecloth.