Nothing like rebooting after upgrading and getting dumped to a busybox prompt to get the blood flowing in the morning... A search of the forums shows this has happened to people in past versions too. Any idea why this happens?

I found the rescue options from a vanilla Debian installer to be the best -- it automatically sees the luks encrypted volumes, asks for passwords, does the cryptsetup seamlessly, asks to change my root for me -- really makes the process as foolproof as it can be. Aside from having to add a nameserver to be able to resolve DNS to be able to run apt install lvm2, it prompted for everything necessary. After running apt install lvm2 and rebooting, everything went right back to normal.

It would be nice if it didn't do that!

Yep, this just happened to me.

The update removed lvm2 (and dependencies) and the lvm2 package seems to be missing from the main neon repo so if you are using disk encryption booting fails.

I was able to boot via grub by selecting an older kernel. I then used sofware&updates tool to temporarily turn on the main ubuntu repo (under 'neon software' tab) and install lvm2 with synaptic.

+1 . Added LVM2 from repo as stated above. I can now boot into 4.4.0-47-generic.

I also ran sudo update-initramfs -u just to make sure, after installing LVM2.