In the StrongLifts report there's a section where the author discusses being able to easily run and jog with moderate endurance if you can squat heavy weight such as 300lb. But I don't buy it. I am sure he is not the only one to have purported this but I'm curious as to if there's any truth to it, given a subject who has never trained in any type of running, and if there's not how people simply believe it.
Anaroebic training does have a positive effect on VO2, or oxygen consumption. The body adapts in this way for a few reasons.
Firstly, intravascular pressure increases during heavy lifts, like when performing squats. Because you have to hold your breath (pretty much) and engage your core, your cardiovascular system responds by increasing blood pressure and increasing the force of the contraction of the left ventricle of the heart.
This results in hypertrophy of the walls of the heart. The official condition is called athlete's heart. This can be bad when extreme (poor electrical conduction of the heart) but problems are rare for most. It's natural and beneficial for most-only a problem if you have a defect or dangerously high cholesterol levels.
Your body responds to aerobic training in a similar manner, although the hypertrophy of the heart isn't as drastic (more likely with sprinters or short distance runners).
Now both types of athletes' bodies have adapted to the overload being placed on the body-it's just a question of how much, and what systems are responding more.
Is that lifter going to be as good as that runner at running a 5K, if all he does is lift? No. But he'll certainly be better off than someone who doesn't exercise at all.
Conversely, that runner isn't going to be able to lift as much, but he'll certainly be better off (cardiovascularly speaking anyway) than a beginning athlete.
Keep in mind that I'm limiting the answer to just the cardiovascular system adaptations for simplicity's sake. There's always more going on!
I should finish off by saying that one must consider what "high endurance" really means. High endurance to a lifter is much different than high endurance to a marathon runner. Remember that our energy systems were built to allow for long distance running (aerobic glycolysis, sweating)-the limitations lie in not knowing where your lactate threshold is (in other words, knowing how to pace yourself), and mechanical inefficiencies (bad form, poor musculoskeletal structure, lack of nutrients). Anybody can run for miles if they know how to pace themselves and are generally healthy. It's how our ancestors hunted after all-keep that in mind.