OK, I have got there. The Display Graphics check box governs the code which enables the instant preview drop-down menu. However, there is a delay -- a behaviour delay, not a time delay -- between selecting the check and getting the drop-down enabled. It is not adequate to Apply and Save. It is necessary to close the whole Preferences dialog and then re-open it. Then the drop-down will be enabled. Likewise when the Check is cleared: the drop-down will only be greyed when the Preferences dialog is closed and re-opened.
Thanks for lyx, it is a superb tool.