I usually use shutdown /reboot from terminal but lxsession-logout is in my menu (openbox).
Recently it hasn't been working but I never waited long enough. Eventually the menu opens up, it only has logout lockscreen cancel on it, the shutdown reboot options are gone. Still will not logout.
I tried lxsession-git to see if it makes a difference, but same exact thing.
It takes about 120sec to respond, maybe more, and on terminal it gives no error.

Any hints on what I should look for?
that's sound as a permissions issues. Do you use consolekit? Do you launch the desktop with it? Consolekit's daemon is running? Maybe polkit issues?
consolekit-daemon is running, lxpolkit is not but that never interfered with lxsession-logout, all rights in ~/ are fine.
lxpolkit is part of lxsession but in openbox you have to use it manually or put it in autostart if it is needed. lxsession-logout worked either way.
When it is run from terminal it does not produce any error, it just take too long and when it appears the shutdown/reboot options are not there. Only logoff cancel and lockscreen.
It shows in tasks as taking up memory but for 2' there is nothing.
Finally I got it to produce an error, not on terminal but a gui note, after I had run lxpolkit:
Error initializing authority: Error calling StartServiceByName for org.freedesktop.PolicyKit1: GDBus.Error:org.freedesktop.DBus.Error.TimedOut: Failed to activate service 'org.freedesktop.PolicyKit1': timed out (service_start_timeout=25000ms)
Also with trying lockscreen I got this:
which: no slimlock in (/usr/local/bin::/usr/bin::/bin::/sbin::/usr/share/man::/opt/::/usr/local/bin:/usr/bin:/bin:/sbin:/usr/share/man:/opt/:/usr/local/sbin:/usr/bin/site_perl:/usr/bin/vendor_perl:/usr/bin/core_perl)
Forget that 25s it takes more than 2 mins to pop out its screen

In all years on openbox/lxde I've never encountered this behavior. It is that stinking freedesktop crap crawling everywhere.
I don't have slimlock or any other screen locker, I never use that stuff.
humm, do you have polkit daemon running?
in your autostart file try to launch this 
/usr/lib/polkit-gnome/polkit-gnome-authentication-agent-1
or another polkit agent
I have polkit installed, I also tried the same thing with with lxpolkit, I tried with sudo or in root's openbox. Same behavior.

It is not that important to me, I only click on this thing when my eyes are closing and I am falling asleep at the terminal, so I am not sure for how long it has been like this or what may have caused it. In other distributions it has more options (reboot shutdown suspend hybernate ... I only use the first two) and it works right away. Here only logoff works and that is after a long while.
Maybe I should dig into the logs.
do you launch your openbox session with ck-launch-session?
what's the output of ck-list-sessions?
I am pretty sure that ck-launch-session is what launches openbox, if I kill it (which I just did) I return to console :)
% ck-list-sessions
Session3:
	unix-user = '1000'
	realname = '(null)'
	seat = 'Seat1'
	session-type = 'unspecified'
	session-class = 'user'
	session-state = 'active'
	active = TRUE
	x11-display = ':6'
	x11-display-device = '/dev/tty1'
	display-device = '/dev/tty1'
	remote-host-name = ''
	is-local = TRUE
	on-since = '2018-06-17T15:59:01.555904Z'
	login-session-id = ''
	XDG_RUNTIME_DIR = '/run/user/1000'
	VTNr = '1'

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