BA don't make it easy for anyone wanting to fly to Luton but not having any idea what routes are available from their partner airlines.
While Luton appears on the airlines drop down list a passenger would have to know which route existed so they could enter a destination. By leaving it blank an option appears called "not sure where or when"
By clicking on that there is a further option called "Find out where we and our partners fly". By clicking on "view by continent" and selecting "UK" Luton does not appear on the list of UK airports.