I did a short weekend investigation (sadly not able to spend much time 
)
The camera hardware is running by default (tested with cheese) in every distro.
Tested before and also after apt-get update && apt-get upgrade.
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Fedora 30 - no camera in LB
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Mint 19.2 - no camera in LB
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Ubuntu 19.04 - no camera in LB
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Ubuntu 18.04 - no camera in LB
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Ubuntu 16.04 - camera working in LB
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16.04 is the last version which contains gstreamer 0.10.36 (end of life) beside 1.8.3 (according to documentation).
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18.04 doesn’t have 0.10xx and is running gstreamer 1.14.5.
I was interested in the differences of the gstreamer stuff in my fresh installed Ubuntu 16.04 and 18.04:
dpkg -l |grep gstreamer* - Ubuntu 16.04
ii gir1.2-gstreamer-1.0 1.8.3-1~ubuntu0.1 amd64 GObject introspection data for the GStreamer library
ii gstreamer1.0-alsa:amd64 1.8.3-1ubuntu0.3 amd64 GStreamer plugin for ALSA
ii gstreamer1.0-clutter-3.0 3.0.18-1 amd64 Clutter PLugin for GStreamer 1.0
ii gstreamer1.0-fluendo-mp3:amd64 0.10.32.debian-1 amd64 Fluendo mp3 decoder GStreamer 1.0 plugin
ii gstreamer1.0-libav:amd64 1.8.3-1ubuntu0.2 amd64 libav plugin for GStreamer
ii gstreamer1.0-plugins-bad:amd64 1.8.3-1ubuntu0.2 amd64 GStreamer plugins from the “bad” set
ii gstreamer1.0-plugins-bad-faad:amd64 1.8.3-1ubuntu0.2 amd64 GStreamer faad plugin from the “bad” set
ii gstreamer1.0-plugins-bad-videoparsers:amd64 1.8.3-1ubuntu0.2 amd64 GStreamer videoparsers plugin from the “bad” set
ii gstreamer1.0-plugins-base:amd64 1.8.3-1ubuntu0.3 amd64 GStreamer plugins from the “base” set
ii gstreamer1.0-plugins-base-apps 1.8.3-1ubuntu0.3 amd64 GStreamer helper programs from the “base” set
ii gstreamer1.0-plugins-good:amd64 1.8.3-1ubuntu0.4 amd64 GStreamer plugins from the “good” set
ii gstreamer1.0-plugins-ugly:amd64 1.8.3-1ubuntu0.1 amd64 GStreamer plugins from the “ugly” set
ii gstreamer1.0-plugins-ugly-amr:amd64 1.8.3-1ubuntu0.1 amd64 GStreamer plugins from the “ugly” set
ii gstreamer1.0-pulseaudio:amd64 1.8.3-1ubuntu0.4 amd64 GStreamer plugin for PulseAudio
ii gstreamer1.0-tools 1.8.3-1~ubuntu0.1 amd64 Tools for use with GStreamer
ii gstreamer1.0-x:amd64 1.8.3-1ubuntu0.3 amd64 GStreamer plugins for X11 and Pango
ii libgstreamer-plugins-bad1.0-0:amd64 1.8.3-1ubuntu0.2 amd64 GStreamer development files for libraries from the “bad” set
ii libgstreamer-plugins-base1.0-0:amd64 1.8.3-1ubuntu0.3 amd64 GStreamer libraries from the “base” set
ii libgstreamer-plugins-good1.0-0:amd64 1.8.3-1ubuntu0.4 amd64 GStreamer development files for libraries from the “good” set
ii libgstreamer1.0-0:amd64 1.8.3-1~ubuntu0.1 amd64 Core GStreamer libraries and elements
ii libreoffice-avmedia-backend-gstreamer 1:5.1.6~rc2-0ubuntu1~xenial9 amd64 GStreamer backend for LibreOffice
dpkg -l |grep gstreamer* - Ubuntu 18.04
un gstreamer0.10- (no description available)
ii gstreamer1.0-a 1.14.5-0ubun amd64 GStreamer plugin for ALSA
un gstreamer1.0-a (no description available)
un gstreamer1.0-a (no description available)
ii gstreamer1.0-c 3.0.26-1 amd64 Clutter PLugin for GStreamer 1.0
ii gstreamer1.0-g 1.14.5-0ubun amd64 GStreamer plugins for GL
ii gstreamer1.0-g 1.14.5-0ubun amd64 GStreamer plugin for GTK+3
un gstreamer1.0-l (no description available)
ii gstreamer1.0-p 1.1.9-1ubunt amd64 GStreamer plugin to install codec
un gstreamer1.0-p (no description available)
ii gstreamer1.0-p 1.14.5-0ubun amd64 GStreamer plugins from the “base”
ii gstreamer1.0-p 1.14.5-0ubun amd64 GStreamer helper programs from th
ii gstreamer1.0-p 1.14.5-0ubun amd64 GStreamer plugins from the “good”
un gstreamer1.0-p (no description available)
ii gstreamer1.0-p 1.14.5-0ubun amd64 GStreamer plugin for PulseAudio
ii gstreamer1.0-t 1.14.5-0ubun amd64 Tools for use with GStreamer
un gstreamer1.0-v (no description available)
un gstreamer1.0-v (no description available)
un gstreamer1.0-v (no description available)
ii gstreamer1.0-x 1.14.5-0ubun amd64 GStreamer plugins for X11 and Pan
There is much less stuff in 18.04 than 16.04.
Mainly plugins are missing. I didn’t had the time to give it a try.
My personal solution at the moment:
Ubuntu 19.04 and Fedora 30 makes my system freeze and unresponsible a few times.
So I switched from my rock stable Mint 19.2 to 16.04 which is running well and it is supported perfectly by Lightburn 
@Doug
An AppImage contains every library which is not included in the distro it is build.
This mean it can fail in other distro’s which has a lighter or very different setup.
There is no guarantee it will run everywhere. The Developer has to check the AppImage in every distro and add more stuff if needed.