Can stretching the lats make you a better runner? Perhaps. It's been well documented that a forward head posture causes a shorter stride length. One reason that forward head posture can creep up is that the body must displace it forward to keep it in balance as the shoulders roll forward. In our flexion dominated society, a pretty easy thing to do. One of the main muscles that can contribute to the forward shoulder is the latissimus dorsi.
Shorten stride length is important from a health standpoint, not just performance. When you shorten your stride length, you have more of a flat foot strike instead of heel strike. So your ankle will take more of a beating.
So grasp a fixed object. Squat back and lean away. With your free arm, rotate through and under your fixed arm. Keep your feet firmly planted on the ground. So the next time you go for a run, try stretching your lats and see if it helps free you up a bit more.