lilyterm auto-completion not work

As stated in the comments to the other answer, first make sure that bash-completion is installed:

sudo apt-get install bash-completion

and apparently for @diapir, it helped to reinstall it:

sudo apt-get install --reinstall bash-completion

However, for me, the problem was not that bash-completion was not installed or broken, the problem was that I had accidently deleted my .bashrc file. You can get a new one by copying it from /etc/skel:

cp /etc/skel/.bashrc ~/