Your post lacks specifics.
You bought the Delock 63928?
You're trying it with the 21.5 inch LG UltraFine 4K display (4096x2304)?
The Delock doesn't include USB and the LG 21.5 inch requires USB.
One person said an ALOGIC USB-C to DisplayPort cable works even though it doesn't have USB but this has not been confirmed by someone else.
Page 10 | Easiest way to drive LG UltraFine 4K Monitor with ...
Page 10 | I am spending much time on looking for a solution to drive LG UltraFine 4K with eGPU. Well, Blackmagic eGPU is fine, but its legacy RX580 is...egpu.io
I can confirm the Alogic USB-C to DisplayPort cable works on a LG Ultrafine 4K 21.5 with an eGPU, don't know how exactly but it does, the only detail is brightness and audio not working, but no much issues there.