Node-RED is based on Node.JS so you need a server that will handle this. Azure is a good choice since support for Node.JS is built in to their web app service. Azure uses IIS of course and you can use the same IIS library they do on your own IIS server.
You can also use a web server such as Apache or NGINX to act as a "reverse proxy" to a Node.JS service such as Node-RED. Doing a search for "apache reverse proxy node.js" or similar should reveal several approaches.
You could, of course, if you control your own server, reveal Node.JS directly to the Internet but this is really not recommended due to the complexities of ensuring security. You may find some additional information on my blog.
Phusion Passenger is a great tool for managing the link from Apache/NGINX and Node.JS apps.