I'm using LG 27inch for 27inch iMac 5K with Thunderbolt to HDMI conversion
After waking up from sleep, the iMac shows the LG display app window for a moment, then after the LG display is activated, the app window does not appear.
Start "System Preferences"> "Display", and once you change the resolution on the LG display, it will be displayed, so you can use it by restoring it again.