Losing an arm generally would not be considered a lucky break for anybody. Obviously, there's pain, blood loss, and risk of infection. For Yeung Gor, however, losing his arm might have been one of the luckiest breaks of his life.
At the time that Yeung Gor lost his arm, he was already in danger of dying of Passion Flower Poison. There wasn't much he could do about it. He basically had two choices: A). wait for his friends and allies to obtain the antidote or B). wait to die. He was in no position to save his own life.
Not until he discovered and learned how to use Dook Goo Kau Bai's Heavy Iron Sword anyway, and consumed snake organs that boosted his inner power exponentially.
Yeung Gor needed his drastically improved martial arts to accomplish many of his pressing goals (i.e. saving Little Dragon Girl and his own life) between the time that he lost his arm and the time that Little Dragon Girl began her sixteen-year separation from him. Without his rapidly improved martial arts, it's doubtful Yeung Gor could have accomplished those goals. Had he not lost his arm, however, he likely would not have returned to Dook Goo Kau Bai's cave and obtained the Heavy Iron Sword, the snake organs, and the new skills that came with the artifacts. Without these, he might not have been able to survive ROCH.
So perhaps losing his arm wasn't the worst thing that could have happened to Yeung Gor? Imagine what might have happened to him if he *hadn't* lost the arm.