Okay, so to answer my own question: thanks to psychedup74's response in the Pine64 thread in this sub-forum I found that the latest image (running kernel 4.19.x) simply does not support the LCD yet (Not yet configured correctly in device tree? I don't know precisely).
To get the Pine64 LCD-screen working with the PineA64-LTS simply use the legacy image running kernel 3.10.x (torrent link). The PineA64-LTS runs butter smooth on it, with working LCD screen, wifi, sound, USB ports, etc. Again, thanks heaps to the Armbian team for making this work so well! You guys rock :)