I've created a bug report for this issue but I am all out of ideas for investigating the cause. Upon restart, lightdm makes 5 attempts to start before failing at the console screen, and anytime that
sudo systemctl restart lightdm is invoked as well. Please see the above link for all attached log files. The last successful reboot was on March 13th, the issue then occurred on March 31st when it was rebooted again.
I have tried purging and reinstalling my Intel graphics drivers. I have tried an older kernel (4.4.0-112-generic). I have also tried purging and reinstalling lightdm and xorg, to no avail. I've also tried refreshing the initrd files:
update-initramfs -c -k all update-grub
I am able to boot into the desktop using lxdm, but many applications will not launch. For example, Firefox always fails with a segfault, Roxterm will not open, Transmission will not open, and aside from the Firefox segfault, these failures are not showing up in syslog or kern.log. Applications that will open inside the desktop environment (LXDE) include Seamonkey, Lxterminal, and PCmanFM.