Leafpub is developed and tested on Apache, but there's nothing stopping you from using another web server. Try Caddy, for example. Caddy is an alternative web server that is easy to configure and use. It's open source, actively developed, and boasts some slick modern features.

Support for Caddy was requested on GitHub, and @calmdev was kind enough to provide a sample config.

example.com {
  root ./app
  gzip
  fastcgi / 127.0.0.1:9000 php
  rewrite {
    regexp ^/backups
    status 403
  }
  rewrite {
    to {path} {path}/ /index.php?{query}
  }
}

Once you've setup your Caddyfile, copy over your existing Leafpub site or run the installer as usual. You'll be up and running in no time.

Need help getting things setup? Try asking on the community forum!