Either skip the usual screen locking options, i.e. don't run gnome-screensaver etc.
If you must, disable the Cinnamon lock screen
$ gsettings set org.cinnamon.desktop.lockdown disable-lock-screen true
Otherwise, just skip ahead to using Ctrl-Alt-L for locking, which will only lock Cinnamon, and not Ubuntu
Edit: that doesn't help either, have to disable it explicitly.