Unfortunately it's currently not supported to display all available lookup items while text is entered in the TAdvLUEdit.
You could try using the OnAsyncChange event instead of the OnAsyncKeyPress but that might be triggered too late if you want to display the value while the user is still typing.
As an alternative you can have a look at the TIWAutoFormFill control (can display a dropdown with available items underneath a default TIWEdit control) or the TIWMultiColumnComboBox (can display a dropdown with lookup and filter options). Both controls have a demo page in the TMS IW FeaturesDemo application.