What version of Windows are you running, XP? If so which service pack do you have installed on it?

lsass.exe service along with a few other critical system processes do appear to access the internet even right at startup, that is normal unless the file in question has been modified/replaced by a worm/virus. Sasser worm or some of its variants would cause the system to shutdown/reboot after 60 seconds if that is not the case then I think you are fine but if you feel your system might be infected, then I suggest you go check out this sticky.

~TL