How do we disable ctrl-alt-del on Ubuntu 16.04?

In the systemd world, CtrlAltDel is handled by ctrl-alt-del.target:

ctrl-alt-del.target
   systemd starts this target whenever Control+Alt+Del is pressed on
   the console. Usually, this should be aliased (symlinked) to
   reboot.target.

To disable this target, do:

systemctl mask ctrl-alt-del.target
systemctl daemon-reload

This does not completely disable CtrlAltDel. Systemd has a feature where pressing that key combination more than 7 times in 2 seconds triggers an immediate reboot. I'm not sure how to disable it, but I find it useful.

I don't think it can be disabled. From the systemd manpage:

SIGINT

Upon receiving this signal the systemd system manager will start the ctrl-alt-del.target unit. This is mostly equivalent to systemctl start ctl-alt-del.target. If this signal is received more than 7 times per 2s, an immediate reboot is triggered. Note that pressing Ctrl-Alt-Del on the console will trigger this signal. Hence, if a reboot is hanging, pressing Ctrl-Alt-Del more than 7 times in 2s is a relatively safe way to trigger an immediate reboot.

systemd user managers treat this signal the same way as SIGTERM.