Indeed, Nate fights with every fiber of his being to run. He snarls in pain as he feels his wrist shatter from the force of Lazarevic's attack, which essentially takes climbing out of the equation. He'd have to run if he wanted to live, and he'd have to run somewhere that wasn't his apartment if he ever wanted to live safely again.

He kicks, he punches with his uninjured hand, and he does so in ways that he hope will incapacitate the Serbian long enough for him to run. He scratches at his face, kicks him in the groin, throws a knee into his stomach, and makes a break for it.

Nate knows he can't win a fistfight with an immortal, so he doesn't try.