I bought a Lilli but they are not that great during the day, especially when its sunny. The touchscreen overlay is responsible for a lot of the dimness. I've just installed a LinITX monitor and that seems brighter and clearer although I haven't done a side by side comparison yet. Maybe it is just down to the touchscreen overlay. I guess you have a few options.
Send it back and try another Lilli
Replace the TS overlay
Buy a different monitor and flog yours on
Wait and see what happens
here and do the mod if it works out ok
If you think it might be the egg, then take mains power out to the car and try that to see if there is a difference.