I am also working on a project using KA Lite.
I believe we have experienced a similar problem to yours. Was the video frame just black when accessing the video page? We also noticed that the video would play in the same browser if a direct link to the mp4 file was given. Is this what happens to you?
In our case, a few Android devices were playing the videos (Android 4.4.1 and older versions of chrome and firefox), while newer devices wouldn't (Android 7, latest versions of chrome and firefox available from the google play store).
So far I haven't been able to determine the problem in the Android tablets, as I still don't know how to use browser developer tools in them, and I don't have access to the devices at the moment.
On a side note: I was testing with different browsers from a Linux desktop (Firefox ESR 52.2.0 (64-bit)), and I noticed that I got a JS error similar to this (it was in portuguese, so I translated it):
Specified attribute "type video/mp4" is not supported. Loading /content/kTiLMIrBWfU.mp4 failed
It is not possible to reproduce this media. There are no decoders for the required format: video/mp4
Perhaps my firefox browser error is similar to what is happening to the Android devices?