You may be interested in NixOS' way. This is all what you need in your configuration.nix to get a webserver running with an SSL certificate from Let's Encrypt, including automatic refreshes before expired and everything:

    services.nginx = {
      enable = true;
      virtualHosts."example.com" = {
        root = "/webroot";
        enableACME = true;
      };
    };

http://nixos.org/nixos/options.html#services.nginx

You can do that with the Lua plugin: https://github.com/GUI/lua-resty-auto-ssl

Is ACME an Internet standard yet? Are there any TLS CA that support it, other than LetsEncrypt?

You should have a look at caddy. Its an alternative to nginx that does exactly that.