Hi! I've had several displayLink monitors including the Lenovo LT1421.
The behaviour of the display depends on your graphics card, your operating system, and the attached displays, so it's a little hard to predict.
In my experience, if you try to run mirror mode, you'll get the smallest native resolution supported with black crop boxes on any display with greater resolution.
So my best guess is:
-- your Beamer will show 1024x768
-- your Lenovo will show 1024x768 -- with two vertical black bars, left and right of 171x768 black unused pixels
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