On fat clients, LDM_SESSION is currently set to the Exec line of the chosen session when X50-generate-env starts (whether passed from the session menu in LDM_SELECTED_SESSION or translated and stored in LDM_SESSION). That worked for GNOME Flashback (Compiz) and GNOME Flashback (Metacity) in GNOME 3.18 in Ubuntu 16.04, but in GNOME 3.28 in Ubuntu 18.04 they both have the same Exec line. According to https://mail.gnome.org/archives/gnome-flashback-list/2018-October/msg00003.html gnome-session.service file uses $DESKTOP_SESSION env to decide which session to start. However, this process is leading to an empty DESKTOP_SESSION when LDM_FORCE_SESSION, .dmrc or LDM_SESSION are set to gnome-flashback-metacity, or when GNOME Flashback (Metacity) is chosen from the session menu. With DESKTOP_SESSION empty, flashback defaults to compiz. When you start your server with Ubuntu MATE, installing gnome-session-flashback pulls in compiz, so you get compiz every time. When you start your server with standard Ubuntu, installing gnome-session-flashback does not pull in compiz, so you get returned to the login screen after a short black screen and spinning cursor. Manually setting DESKTOP_SESSION to gnome-session-metacity works around this, but makes it impossible to select any other session. For future compatibility, it appears it would be better for LDM_SESSION to keep the name of the session file.
What is the output of sudo ltsp-info?