Adventurous gunsmiths may have attempted all sorts of things. VonGruff's project looks interesting! (Please keep us posted).

But you are correct that the Lee-Speed was never chambered in .405 from (any) factory.

I am a HUGE admirer of John Walter, but in this particular instance ("Rifles of the World") he is incorrect about Lee-Speed chamberings. He either misread the catalogue (understandable in this case; the info is presented in a way that is easily misconstrued), or a few numbers got jumbled in the final edit. It happens.