Since I have found some issues with my previous LXQT setup in real-life work I decided to fall back to standard Lubuntu for my cloud desktop. As part of this I also switched to TightVNC which seems a lot easier to configure.
Add local user account
adduser USERNAME sudo
Install Lubuntu Desktop
sudo apt-get install --no-install-recommends lubuntu-desktop tightvncserver
sudo vim /etc/lightdm/lightdm.conf
# VNC Server configuration
# enabled = True if VNC connections should be allowed
# port = TCP/IP port to listen for connections on
sudo /etc/init.d/lightdm restart
Connect to the remote system
ssh -L 5900:localhost:5900 -i /path/to/your/aws/keyfile.pem YOUR.EC2.IP.ADDRESS
If you are using a Chromebook then this article might help.