In an 8- to 10-quart pan, bring broth to a boil over high heat. Meanwhile, pull off and discard coarse outer layers from lemon grass and trim off and discard stem ends; rinse lemon grass. Cut each stalk into about 3-inch lengths. With the flat side of a knife, lightly crush lemon grass and ginger. Rinse chilies and cut one or two in half lengthwise (use two if you'd like it spicy); stem remaining chilies (seed, if desired, for less heat), finely chop, and reserve. Add lemon grass, ginger, and halved chilies to boiling broth. Reduce heat and simmer, covered, for 20 to 30 minutes.
Meanwhile, rinse cabbage and cut into shreds about 1/4 inch wide and 2 to 3 inches long. Rinse mushrooms, trim off and discard stem ends and discolored parts, and slice lengthwise 1/4 inch thick. Peel carrots and slice 1/4 inch thick. Rinse chicken and cut into 1/4-inch-thick slices 1 1/2 to 2 inches long.
With a slotted spoon, remove and discard lemon grass, ginger, and chilies from broth.
Add cabbage, mushrooms, carrots, and garlic to broth; cover and bring to a boil over high heat. Reduce heat and simmer until carrots are tender when pierced, 8 to 10 minutes.
Add chicken and tomatoes (including juice). Cover and cook over high heat until chicken is no longer pink in the center (cut to test), 2 to 4 minutes. Add lemon juice and fish sauce to taste. Serve soup from the pan, or pour into a tureen. Sprinkle with green onions.
Place rice, lemon wedges, cilantro, and chopped chilies in separate bowls and offer with soup to add to taste.