This might already be obvious to most of you, but the reason why a lanyard on a FJ knife was a good idea, is that those knives were sometimes needed in emergencies, like tree landings. When hanging suspended in a tree, it was often necessary to cut the harness or suspension lines, to get down to the ground. Dropping one's knife in that situation would be disastrous. Having the knife attached to a lanyard would allow a paratrooper to retrieve the knife in case that happened.
I know that some American paras also attached a lamnyard to the smaller M2 switchblade jump knife they carried in a special small pocket below their neck. To my knowlegde such US Para M2 knife lanyards were 'Improvised' and not mass-produced-at least not as early as WWII.
There is some photo evidence that these were worn, but I have never seen nor received one with any of the dozen or so M2 knives I've acquired from the 992 101st Airborne vets I've interviewed in the past 38 years. So I'd say that WWII vintage, improvised M2 knife lanyards are even less-common than German gravity knife lanyards.