I was following these instructions to enable unattended upgrades to Lucid, and I hit a known bug with the unattended-upgrades package: the default runlevels for Start and Stop are wrong. I found this page, which suggested the following fixes, which worked.

Symptom: after installing the unattended-upgrades packages, you get this:

update-rc.d: warning: unattended-upgrades start runlevel arguments (none) do not match LSB Default-Start values (0 6)
update-rc.d: warning: unattended-upgrades stop runlevel arguments (0 6) do not match LSB Default-Stop values (none)

Solution:

sed -i 's/Default-Start:[\t ]*0 6/Default-Start:/' /etc/init.d/unattended-upgrades

sed -i 's/Default-Stop:/Default-Stop:\t\t0 6/' /etc/init.d/unattended-upgrades 

dpkg-reconfigure -u unattended-upgrades

Following that, I edited /etc/apt/apt.conf.d/50unattended-upgrades to enable both security and regular updates, and to allow reboots when required. Jenkins seems to cope OK with reboots.