Some running coaches will tell you to lean. Some running methods will also tell you to lean (chi-running, POSE method, etc.)
They tell you that if you lean forward, your feet will catch your fall, and voila, that’s running. They explain that “running is a constant fall”.
(And, seriously, is that what you want your running to feel like, like you are falling??? I want to FLY!)
Leaning as a cue does not work. 90% of runners don’t do it right.
You’re supposed to lean at the ankles. And as hard as you try, if you “think” about leaning, you’ll lean at the hip, or the waist. The posture breaks down, then you have to overstride to catch the “falling”. Leaning does NOT work as a posture cue.
There IS a natural lean that happens when running, but that cue does not work as way to improve your posture.
More on Running Biomechanics