I think the LSR idea probably comes from the ways in which Lydiard's methods were popularised for non-elite runners. When Lydiard was coaching international-quality athletes, he would have them running 100 miles per week or more. When you're running that kind of mileage, there's a natural moderation of speed - you can't go hard on every run and recover in time for the next day, so you fall into a steady aerobic pace.
When Lydiard's ideas were passed on to novice runners who were doing much lower mileages, they didn't have the natural regulation of speed that comes with heavy training. If you're doing, say, 3 miles 3 times per week, then you can get away with running hard every time. I think that most beginners tend to run too hard (I know I did). When I've run with novice runners, who I've been trying to help into the sport, I've often had to tell them to slow down, because they're running too hard relative to their own fitness level. Beginner runners need to learn that running "slowly" (as it feels to them) is ok. As experience and fitness increase, then you can learn to use different paces more effectively.
I guess what I'm saying is that "slow" running is a useful way of thinking for inexperienced runners. For the more experienced, "steady" is a better word.
Interestingly, Lydiard did recommend slow running to his elite athletes, but only as a supplement to their main diet of steady aerobic running. He believed that slow runs brought extra benefits in endurance and aerobic conditioning as well as helping the athlete to recover from the main training. For what it's worth, I think he got that about right.