I got this error, for all gem that I try to install:
ERROR: While executing gem ... (Gem::FilePermissionError) You don't have write permissions into the /var/lib/gems/1.9.1 directory.
obs. I'm running on Ubuntu 14.
According the question I see a few steps in order to allow writing to /var/lib/gems:
Create gems (if not any) group, and add yourself to the group:
$ groupadd -f gems
$ usermod -aG gems $(whoami)
When reenter to the session:
$ sudo -u $(whoami) bash
Allow write for a gems group to /var/lib/gems/, and set the setgid bits:
$ chown :gems /var/lib/gems/
$ chmod g+sw /var/lib/gems/
Try installing gems into /var/lib/gems/.
NOTE: I strongly advice you to control rubies and gems via rbenv/rvm keeping them in a local home folder. Please refer to the answer to know how to properly setup your project.