Hello,
Yes, you are right - I have completely overlooked that you refered to the GridLookUpEdit.
After having a deep look into the DXperience sources I found that it's not a simple task. I only can suggest to create a custom editor derived from GridLookUpEdit.
Please have a look into the following Support Center issue: Change GridLookUpEdit popup window size at runtime
You may also consider to add a suggestion to the Support Center in this regard.
Hope this helps,
Holger