Bring broth to a boil in a saucepan; add zucchini, potato, and onion. Reduce heat to medium-low, cover the saucepan, and simmer until vegetables are tender, about 15 minutes.
Beat eggs and lemon juice together; add 1/2 cup of the hot broth from the saucepan and beat to temper the eggs. Pour the egg mixture into the broth in the saucepan. Increase heat to medium; cook, stirring constantly, for 1 minute. Remove saucepan from heat, stir dill into the soup, and season with salt and pepper.