I think they're fine, as long as you give them sparingly. They also have plenty of sugar, and might be a little bit rich for Lucy. I give Gonzo about 1/2 banana a week, and he LURVES nanas too!! Try mixing half a banana with a tablespoon or two of peanut butter and Milkbone pieces, stuffing it in her Kong and freezing for a few hours. She will LOVE that, it's Gonzo's favorite Kong recipe