CLPM is an interesting project but not used very often since projects rarely version anything in the CL ecosystem (not even branch tags anymore). Personally, I have never seen a library that suggests CLPM for installation.
Roswell is a CLI tool that manages Common Lisp installations, with Quicklisp set up automatically.
Never heard of Qlot or Docker being used.
My biggest gripe is the fact Quicklisp is widely used and no notion of version dependencies exist (not even lockfiles exist). So Common Lisp code with tons of Quicklisp dependencies tends to rot really fast. e.g. it's practically impossible today to build projects like https://github.com/akamai/cl-http2-protocol