Last night I got an updated kernel from stretch-backports (4.15). I was running the 4.14 from there without any issues. On my boxes with Nvidia drivers they all refused to start up the desktop complaining about lighdm has stopped working. My intel-GPU machines were fine so it seems to be the combination of the Kernel + Nvidia drivers

After reinstalling one box I discovered an easier way assuming you can login to the machine by some other method (ssh).

After it reboots and the desktop gets stuck with the lightdm failure message, login via ssh to it. As root remove the nvidia-kernel-dkms and reinstall it:

apt remove nvidia-kernel-dkms -y
apt install -t stretch-backports nvidia-kernel-dkms linux-headers-amd64 -y
nvidia-xconfig

Reboot and lighdm should now work. You probably don't need to redo the nvidia-xconfig but that's what I normally do after a Nvidia driver update.

---

BOINC blog