Let's Encrypt does not endorse website-based ACME clients, as those cannot be automated. And Let's Encrypt is all about automation.
That said, @griffin has build a PHP based ACME client which can be "installed" (read: just download it and put it the webroot of your site) on your website to actually provide a web-based GUI to the client itself. Which might be exactly what you want?
You can read more about this client here: CertSage ACME client (version 1.0.0) - easy webpage interface, no commands to type, root not required