I think serverless refers to the use of 'lamdas' as the unit of deployment, as oppose to containers or VM's, but someone else may want to add/edit that.

README is not quiet clear, but for my understanding, lambda is kinda thing that helps you to do serverless, but lambda is also running on some kind of server maintained by AWS, right? fx is kind of lambda, but owned by yourself.

Well, yes, you can run your own server to provide yourself a serverless platform, but it kind of defeats the purpose... Since then you end up having to maintain your server anyway.

I suppose there may be a point to it if the serverless platform is extremely stable and never has any security issues or other things to update.

Well, the server is abstracted away and vanishes in a puff of logic, you see.