User's cron job not launched when logged out

[Elbarbudo]

On different machines, I discovered that the user's cron job where NEVER executed when user is loggued out.

patrice@nc6000:~$ crontab -l
# added by lico-update.sh version 0.3.17
49 11 * * 4 /usr/local/bin/lico-update.sh -m
10 0 * * * echo `date` > JALON/`date +\%Y-\%m-\%d_\%H:\%M:\%S`_NC6000
10 2 * * * rm JALON/*NC6000

# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ luckybackup entries ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
10 1 * * * env DISPLAY=:0 /usr/bin/luckybackup --silent --skip-critical /home/patrice/.luckyBackup/profiles/default.profile > /home/patrice/.luckyBackup/logs/default-LastCronLog.log 2>&1
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ end of luckybackup entries ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
patrice@nc6000:~$

Everything runs fine when user is logged in.
NOTHING happens when user is logged out.

ProblemType: Bug
DistroRelease: Ubuntu 12.04
Package: cron 3.0pl1-120ubuntu4
ProcVersionSignature: Ubuntu 3.2.0-55.85-generic 3.2.51
Uname: Linux 3.2.0-55-generic i686
ApportVersion: 2.0.1-0ubuntu17.5
Architecture: i386
Date: Sat Oct 12 08:02:19 2013
InstallationMedia: Ubuntu 12.04 LTS "Precise Pangolin" - Release i386 (20120423)
MarkForUpload: True
ProcEnviron:
 TERM=xterm
 PATH=(custom, no user)
 LANG=fr_FR.UTF-8
 SHELL=/bin/bash
SourcePackage: cron
UpgradeStatus: No upgrade log present (probably fresh install)

[Elbarbudo (patricearnal)]

Same thing on a 64bits machine