The default command used by the system menu is;
lxde-logout
or
lxsession-logout

This command just opens the menu options you have seen before.

Start with opening a terminal (Alt + X) type in at the prompt;
shutdown -P now

If that worked, then we need to configure the menu to use that command instead of the default lxde-logout.  LXpanels are in charge of the menu plugin button option. It is not easy or simple to edit.  The simple option would be to edit the logout.desktop shortcut or add a custom shutdown of your own to the existing menu.  I will post how this is done, if needed, on a later reply.

Another route I would try, a logout to the LightDM greeter. (Menu - Logout - Logout) Now up in the upper right corner is a power icon.  If this works, it creates an extra step, but now you know the issue is within the LXLE session and not deeper within the system.

Still rebooting?

As Root user edit the file; /etc/systemd/logind.conf

Assuming there is a power key on your keyboard, edit this line.
#HandlePowerKey=poweroff

Just remove the "#" to turn it on with the next reboot.

No power key available?
#HandleLidSwitch=suspend
HandleLidSwitch=poweroff

That about covers most of what I know, the next stop and last stop, would be your BIOS settings.  If you know how to start the BIOS settings at start up, browse in the power management menus.

Here is the link to the topic I just created about powering down.
https://www.lxle.net/forums/discussion/1763/fast-reboot-and-power-down-now