Arthur would most likely have said; "Any running you can do would be of benefit. There is no such thing as 'junk mile'." He would have also said, and had said it this way, that it is the continuous running that gives you the best results as far as capillary development, therefore muscular endurance development, is concerned. Again, some people might take this as him saying "if you devide your runs, it's not Lydiard"; but it ain't so.
Think of "whys"; Why do some people run three times a day? Time constrain, injury possibility from pounding, emphasize quantity, etc. Didn't John Walker have some strange problem that, after running about 30 minutes, his knee started to give. Make sense to do three or four times of 30-minute segments. Why do some do long continuous run? Just get it over with once (don't have to keep changing!), better capillarization, can't afford to get out twice a day... Some people may take a long time (45 minutes or so) till they finally get warmed up and start to feel good. For the case like that, it does not make sense to have two or three 45-minute sessions; you're just about to warm up by then--you'll miss out all the vital part of workout.
I've personally found out that, if I do go for an easy jog in the morning, I feel much better in the evening (or main training session). Sometimes I'd even go out after the morning long run on Sunday just to stretch out and shake some stiffness out and it felt good. I know Mr. Rono used to, when he was at his top form, run something like 8-mile in AM and 8-mile PM up and down the Snake River in Pullman with a single long run on weekend. Snell, before he would tackle 100MPW, might do 30 minutes in AM with 60 minutes in PM. Chugoku-Electronic (where Ogata, the bronze medalist from Helsinki runs, runs for) did a training camp in NZ (Nelson where Rod Dixon is from) with 3-a-day training regime for about 2 weeks. They would do 60-60-90~120...something like that. Basically LOTS OF RUNNING.
In fact, I've been checking Mr. Rono's training thread and copying his comments and training pattern. I'm amazed how simple and effective it is; basicaly lots of running of total of 120~180 minutes a day! Do it once, twice, three-times (a lady!)... How much more simple can it be?