This seems to be a known issue with DNG, and it affects other RAW capture programs as well. So it seems to be something related to iOS or the iPhone X, and not specifically Lightroom.
You can can work around this by switching to JPG when you need to use flash; and we can hope Apple will help apps to enable this soon.
"Mike: and it affects other RAW capture programs as well"
Before I posted this question to the forum I tried the same with 645Pro - application what I am using for a very long time. It also supports DNG. I don't know how it works but you may use flash with the back camera. However, Exif informs "flash did not fire" even you may see the flash activity on the picture. :-)
It seems to be something really wrong with X.