I think you're massively reaching to bring race into the Ole/Lampard appointments. Giggs is mixed race and would have been handed the United job if LVG didn't royally screw it up.
As I said above there are examples of non-white managers that have as much or more experience than Ole/Lampard or other names thrown into the hat for those jobs but didn't have the same pathway to it despite displaying traits that people are saying why they got the job aka ex-players and did a good job at this club etc.
I'm not saying that they specifically got the job because they are white but using them as an example of cases where there were alternatives but the same opportunities don't seem to have been afforded which is why something like the Rooney Rule would be good or could be implemented better.