If you want to run the Synaptic packet manager in Ubuntu/Lubuntu without it requiring a password, you must add a PolicyKit local definition. For this purpose create a file, named for instance /etc/polkit-1/localauthority/50-local.d/allow-user-update-wo-password.pkla, and add the following content to it:
[Allow User Updates Without Password]
Identity=*
Action=com.ubuntu.pkexec.synaptic
ResultAny=no
ResultInactive=no
ResultActive=yes
