As far as I can tell, XDG_CURRENT_DESKTOP is used to determine autostart process, not DESKTOP_SESSION.
Either way, both environment variables are not set by openbox. DESKTOP_SESSION might be even contaminated by DM, i.e. DESKTOP_SESSION=lightdm-xsession Same goes for yet another var, XDG_SESSION_DESKTOP=lightdm-xsession. I will file another bug against openbox package with my observations and improvement suggestions.
