Running is generally considered a high intensity activity, but of course there are different degrees.

>"The definition of high intensity training is literally anything above that (lactate) threshold."

That's far from a universal definition. The phrase "high intensity training" often refers to a type of strength training popularized by the founder of Nautilus that involved lifting until muscle failure. What you're describing specifically is called anaerobic training.

> That's far from a universal definition.

In sports medicine lactate threshold/anaerobic threshold/90(ish)% of VO2max has been the de facto definition for high intensity efforts for many many years.

You'll find plenty of examples on Google Scholar (including papers criticizing people for using these thresholds to define the intensity of workouts...)

> Running is generally considered a high intensity activity

Nope. Running can be a low, medium or high intensity activity depending on how hard you run (relative to your max).

That's an extremely pedantic argument. This isn't a sports medicine journal and you can google to find many other sites focused on health and wellness that go with a more mainstream usage. This even includes the NIH for what it's worth but I'm done on this thread.