Why the weird lag in Screen Sharing app when using the LG Ultrafine 5K monitor? Hardware:

Late 2016 MacBook Pro w/ TouchBar
LG Ultrafine 5K display

Setup:

Screen Sharing app connected to remote instance in the cloud

Problem:

Very slow response to keystrokes.  There is no problem in other applications.   The problem goes away if I disconnect the external display.  The problem does not go away if I switch from WiFi to a hardwired Ethernet connection.  I had thought this might be the monitor's shielding problem interfering with WiFi but no, it happens without WiFi.  Truly perplexing!
Apple's implementation of VNC ScreenSharing often falls short, with significant lag regardless of whether Adaptive Quality is selected or not. A more robust 3rd-party solution like (the free) VNCViewer will provide you with fine-grained compression control, allowing workable VNC sessions over the tightest of bandwidth (e.g. through a shell tunnel to a remote server with really low upload speeds).