After not being able to actually find the particular problematic interaction between Debian 9 lightdm and the cygwin XWin server, and after a bit more thought, I thought I'd investigate possible workarounds. The main point seemed to be whether or not some other display manager would exhibit the same behavior as lightdm.
After some investigation I decided to look further at the following display managers: xdm - the original X11 display manager wdm - a WINGs widget update of xdm sddm - update of kdm, the KDE display manager gdm3 - Gnome display manager, already installed by default on Debian 9. lightdm - downgraded version from Debian 8. It turns out that xdm does work with an XDMCP connection from cygwin XWin. However the aesthetics are a bit dated and there is some sort of drawing synchronization issue when updating the login dialog box. It takes quite a few seconds to update the dialog seemingly one scanline at a time. Also there is an audible whine coming from the monitor when this is happening. Overall, not really acceptable. wdm is quite an improvement over xdm. No drawing synchronization issues, very snappy feeling in general, no audible whine. The only weakness is the aesthetically dated UI. I can live with that. sddm had quite a few KDE style dependencies so since wdm was quite acceptable I decided not to look further at sddm and didn't even install it. gdm3 did function, sort of. Login was possible but then some sort of additional authentication was required in order to set the color depth of the display. Since the overall response was really quite slow, I didn't investigate further as wdm, dated look and all, was superior to such a slow response time as exhibited by gdm3. lightdm from Debian 8, oldstable, did not function properly in the Debian 9 environment. Instead of drawing one blank screen like when connecting to the Debian 9 lightdm, XWin, when connecting to the Debian 8 lightdm, would continually redraw its window decorations but still not draw any login dialog. Certainly not useful. So bottom line, I'm now using wdm at the Debian end when remotely connecting to Debian 9 machines from a cygwin XWin server. This is quite acceptable in that the only downside is the dated login UI. Since I mostly just use a terminal and ssh/putty anyway, any slight problem with XDMCP connections isn't really an issue.
