Same with MBP 16" 2019. Working just fine with the latest Catalina as far as I can remember.
The external LG (HDMI to USB-C or HDMI to Hub via USB-C) works fine after reboot, when computer sleeps and wakes up, it blinks a couple of times, then switches off. The open windows remain on the external display although it's off, and there's no way to turn back on the LG unless I reboot the Mac