Hello,
The list of resolutions (or more exactly modes/timings) depends on the panel and what the manufacturer has programmed in the product. DisplayLink driver receives the timing from the product, and selects the preferred resolution advertised.
Using 1366 on a 1920 would look dreadful though because pixels are either ON or OFF. Because they are identical, double or half of each other, it means you would get fuzzy text, or broken lines: see details in
https://en.wikipedia.org/wiki/Native_resolution
That would alone be a reason for the manufacturer not to wish to advertise modes which would create negative feedback on their product.
If you send me the .EDID file in the DisplayLink software folder, I can parse it and indicate which modes the monitor advertise supporting.
Kind regards,
Alban