I successfully installed Pi-hole on a thin VM with Alpine Linux (Virtual), here are the steps I took to do so, you should be able to adapt those to install to any compatible Linux distro:
Pi-hole FTL installation: pihole-ftl_installation.txt (1.6 KB)
If you're installing on Alpine Linux, first follow the steps to setup Nginx with PHP 7: https://wiki.alpinelinux.org/wiki/Nginx_with_PHP#Nginx_with_PHP7
If you're installing on another Linux distro with systemd, you can grab systemd compatible service files from: https://aur.archlinux.org/packages/pi-hole-ftl
Pi-hole AdminLTE installation: pihole_installation.txt (4.3 KB)
For some reason, on Alpine Linux, the sudo would keep asking for a password when executed from PHP, which would break the admin panel's functionalities, unless I specified ALL applications...
Which means there is no reason that the official Pi-hole Docker image to use Debian as a base, I hope they will switch to Alpine in the future since it has a lot less overhead. 