Place ham bone, stock water, onion, celery and bay leaf in an 8-quart pot. Bring to a gentle simmer, skim foam and cook partly covered for 2 to 2 1/2 hours until the meat loosens from the bone.
Lift the bone onto a tray. Strain the stock, discard spent vegetables and bay leaf, skim excess fat and measure 7 cups liquid, adding water if needed.
Pull usable meat from the bone once cool enough to handle. Discard bone, gristle and excess fat and tear the meat into small pieces.
Heat oil in a clean soup pot over medium-high heat. Brown mushrooms for 6 to 8 minutes, then add the measured stock, barley, thyme and pepper.
Simmer partly covered for 25 minutes, then add green beans, the meat from the bone and the measured extra ham. Simmer for 15 to 20 minutes more until barley and beans are tender and ham reaches 165°F.
Stir in lemon juice and divide among six bowls, distributing the barley, vegetables and meat evenly.