How To: Get LetsEncrypt working with IIS manually

You don't need a Linux system unless you really want to run the official reference client. There are some nice community contributed options, including a PowerShell option and a very alpha-state GUI. See List of Client Implementations.

It does, with some registry key changes. If you don't want to mess around there, you can look at IISCrypto, which is a nice GUI for doing the same thing. I'm using it on our older systems with success.