Solution 1:

You can get more lightweight than LXDE by using just a window manager like fluxbox, openbox, i3-wm or awesome from the default Ubuntu repositories instead of a desktop environment.

To install Fluxbox and a few additional packages like in the below screenshot, open the terminal and type:

sudo apt install lightdm xorg fluxbox catfish eterm hsetroot xloadimage fbautostart fbpager wm-icons
sudo reboot  

enter image description here

Solution 2:

I would recommend that you check out the i3wm (i3 window manager). Apps fill the screen by default, and it is highly customizable. Here is a good tutorial.