This feature is available in all editions.
Yes, of course it can! On-Demand instances can be accessed securely using HTTPS. You will receive an the URL once your system is set up.
To run via HTTPS in an Onsite instance, simply install Lifecycle on a webserver that already allows HTTPS. If you must enable it yourself, see the Microsoft IIS documentation for your web server for information about obtaining a digital certificate, enabling SSL on your server, and utilizing secure HTTPS connections for your application.