Just doing an "apt-get dist-upgrade" on a 16.04 VM:

...
Setting up grub-common (2.02~beta2-36ubuntu3.11) ...
Installing new version of config file /etc/grub.d/10_linux ...
update-rc.d: warning: start and stop actions are no longer supported; falling back to defaults
Setting up grub-pc-bin (2.02~beta2-36ubuntu3.11) ...
Setting up grub2-common (2.02~beta2-36ubuntu3.11) ...
Setting up grub-pc (2.02~beta2-36ubuntu3.11) ...
Installing for i386-pc platform.
File descriptor 3 (pipe:[136263]) leaked on vgs invocation. Parent PID 18940: grub-install
File descriptor 3 (pipe:[136263]) leaked on vgs invocation. Parent PID 18940: grub-install
File descriptor 3 (pipe:[136263]) leaked on vgs invocation. Parent PID 18940: grub-install
Installation finished. No error reported.
Generating grub configuration file ...
Found linux image: /boot/vmlinuz-4.4.0-83-generic
Found initrd image: /boot/initrd.img-4.4.0-83-generic
Found linux image: /boot/vmlinuz-4.4.0-21-generic
Found initrd image: /boot/initrd.img-4.4.0-21-generic
done
...
Setting up initramfs-tools-core (0.122ubuntu8.8) ...
Setting up initramfs-tools (0.122ubuntu8.8) ...
update-initramfs: deferring update (trigger activated)
Setting up mdadm (3.3-2ubuntu7.2) ...
update-initramfs: deferring update (trigger activated)
Generating grub configuration file ...
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19859: grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19859: grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19899: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19899: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19909: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19909: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19919: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19919: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19929: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19929: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19979: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 19979: /usr/sbin/grub-probe
Found linux image: /boot/vmlinuz-4.4.0-83-generic
Found initrd image: /boot/initrd.img-4.4.0-83-generic
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 20061: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 20061: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 20072: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 20072: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 20082: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 20082: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 20092: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 20092: /usr/sbin/grub-probe
Found linux image: /boot/vmlinuz-4.4.0-21-generic
Found initrd image: /boot/initrd.img-4.4.0-21-generic
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 20335: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on vgs invocation. Parent PID 20335: /usr/sbin/grub-probe
File descriptor 3 (pipe:[140340]) leaked on lvs invocation. Parent PID 20417: /bin/sh
done
update-rc.d: warning: start and stop actions are no longer supported; falling back to defaults
...

It updated 119 packages, but lvm2 was not one of them.