I removed the files, video, photos and friends lenses with the following command.

sudo apt-get purge unity-lens-files unity-lens-video unity-lens-photos unity-lens-friends

Although the corresponding results have disappeared from dash, only the friends tab has been removed.

There still are tabs for files, video and photos, albeit empty.

How do I remove these empty tabs? I use Ubuntu 13.10 Saucy Salamander.

I understand that this issue didn't exist in 12.04. The directory structure of unity lenses seems to have changed from 12.04 to 13.10. Earlier the lenses were stored in /usr/share/unity/lenses/. That isn't the case now, rendering this answer inappropriate: http://askubuntu.com/a/120116/111720