That is the proper runlevel for a graphical boot... I don't think there can
be a problem in the script but let see anyway: can you show us the beginning
of /etc/init/lxdm.conf (the lines with "start on" and "stop on")?
Enabling Trusty's graphical stack is not hard nor dangerous (easy to revert
if something becomes wrong but it should not: it is the graphical stack of a
long-time-support version of Ubuntu after all!). However, it does not look
like your graphical stack is the problem since 'sudo start lxdm' brings you
the graphical login screen. It only looks like the 'init' does not
automatically start LXDM for some reason.
Unless someone else has a solution, the fix I propose is to write 'start
lxdm' in /etc/rc.local (before the 'exit' line).
