Hello all,
I am an retired engineer, living in San Jose, California.
I enjoy computers, Linux and the nice weather here.
I also do some remodeling for myself and my kids.
Finally, last but not least, I play classical organ, believe it or not.
I have been running Linux on several computers because Linux is the only operating system running on IBM based architecture AND Apple MAC. So, with Linux, I have to support only ONE operating system on several - different - computers.

With a fresh installation of F26 worktation with lxqt, I found two issues:
1 - SELinux prevents the vncserver daemon to run. This is bug (on buzilla) #1412468. The solution is to run as root:
ausearch -c 'systemd' --raw | audit2allow -M my-systemd
semodule -i my-systemd.pp
After rebooting, you can run: (as user, for display #3 with SELinux enforcing)
sudo systemctl start vncserver@:3.service
2 - After fixing SELinux, you can connect with vncviewer but the screen is dark blue. I tested it on the same computer running vncserver with:
vncviewer :3 (easier to debug)
It executes ~/.vnc/xstartup, which executes /etc/X11/xinit/xinitrc
xinitrc executes /etc/X11/xinit/Xclients which, in the fresh installation, does not support lxqt. The solution appears to be to add lxqt support in that file. It requires two things:
a) create /etc/sysconfig/desktop as root. the file content is:
DESKTOP="LXQT"
set the permissions , as root: chmod 644 /etc/sysconfig/desktop
b) modify /etc/X11/xinit/Xclients to add lxqt. Here is the content of the modified file:
#!/bin/bash

Copyright (C) 1999 - 2004 Red Hat, Inc. All rights reserved. This

copyrighted material is made available to anyone wishing to use, modify,

copy, or redistribute it subject to the terms and conditions of the

GNU General Public License version 2.

You should have received a copy of the GNU General Public License

along with this program; if not, write to the Free Software

Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

GSESSION="$(type -p gnome-session)"
MSESSION="$(type -p mate-session)"
STARTKDE="$(type -p startkde)"
STARTLXDE="$(type -p startlxde)"
STARTLXQT="$(type -p startlxqt)" # Added for LXQT

check to see if the user has a preferred desktop

PREFERRED=
if [ -f /etc/sysconfig/desktop ]; then
. /etc/sysconfig/desktop
if [ "$DESKTOP" = "GNOME" ]; then
PREFERRED="$GSESSION"
elif [ "$DESKTOP" = "MATE" ]; then
PREFERRED="$MSESSION"
elif [ "$DESKTOP" = "KDE" ]; then
PREFERRED="$STARTKDE"
elif [ "$DESKTOP" = "LXDE" ]; then
PREFERRED="$STARTLXDE"
elif [ "$DESKTOP" = "LXQT" ]; then # Added for LXQT
PREFERRED="$STARTLXQT" # Added for LXQT
fi
fi

if [ -n "$PREFERRED" ]; then
exec "$PREFERRED"
fi

now if we can reach here, either no desktop file was present,

or the desktop requested is not installed.

if [ -n "$GSESSION" ]; then
# by default, we run GNOME.
exec "$GSESSION"
elif [ -n "$STARTKDE" ]; then
# if GNOME isn't installed, try KDE.
exec "$STARTKDE"
elif [ -n "$STARTLXDE" ]; then
# if neither GNOME nor KDE then LXDE
exec "$STARTLXDE"
elif [ -n "$STARTLXQT" ]; then # Added for LXQT
# if neither GNOME nor KDE nor LXDE then LXQT # Added for LXQT
exec "$STARTLXQT" # Added for LXQT
fi

We should also support /etc/X11/xinit/Xclients.d scripts

XCLIENTS_D=/etc/X11/xinit/Xclients.d
if [ "$#" -eq 1 ] && [ -x "$XCLIENTS_D/Xclients.$1.sh" ]; then
exec -l $SHELL -c "$SSH_AGENT $XCLIENTS_D/Xclients.$1.sh"
fi

Failsafe.

these files are left sitting around by TheNextLevel.

rm -f $HOME/Xrootenv.0

Argh! Nothing good is installed. Fall back to twm

{
# gosh, neither fvwm95 nor fvwm2 is available;
# fall back to failsafe settings
[ -x /usr/bin/xsetroot ] && /usr/bin/xsetroot -solid '#222E45'

if [ -x /usr/bin/xclock ] ; then
    /usr/bin/xclock -geometry 100x100-5+5 &
fi
if [ -x /usr/bin/xterm ] ; then
    /usr/bin/xterm -geometry 80x50-50+150 &
fi
if [ -x /usr/bin/firefox -a -f /usr/share/doc/HTML/index.html ]; then
    /usr/bin/firefox /usr/share/doc/HTML/index.html &
fi
if [ -x /usr/bin/twm ] ; then
    exec /usr/bin/twm
fi

}
After these changes, I rebooted the system and vncviewer worked fine.