Sounds like there's perhaps some confusion around terms which could be what's tripping you up. A Landing Page is designed to be a standalone web page - it's a URL that you can direct folks to, but it lives on its own and is not part of another webpage. If you want to add an email capture box to part of a different webpage, what you're looking for is a Form. Forms will have an embed code that can be added to your existing website (and there are other ways to integrate them with your site as well such as the ConvertKit WordPress plugin).
Was it a Form that you were trying to integrate?