Combine first 6 ingredients in large saucepan. Using vegetable peeler, remove peel from lemon (yellow part only). Add peel to broth mixture. Bring mixture to boil; reduce heat and simmer until neck and gizzard are tender, about 45 minutes.
Remove neck, heart, and gizzard from broth; finely chop heart and gizzard. Pull meat from neck and chop. Strain broth. Return broth to pan; boil until reduced to 3 cups, about 10 minutes. Remove from heat; add tea bag. Cover; steep 10 minutes. Discard tea bag.
Melt butter in heavy medium saucepan over medium heat. Whisk in flour. Cook until light brown, stirring frequently, about 5 minutes. Whisk in broth and cream. Bring to boil; reduce heat to medium and simmer until slightly thickened and smooth, stirring frequently, about 8 minutes. Stir in grated peel and neck, heart, and gizzard pieces. Season with salt and pepper.