As a teenager Lim won three junior/youth national championships and participated in the 2011 Junior World Championships. He received his first call-up to the Korean national team in March 2014 and made his debut at the prestigious in Germany that spring, losing to Vitaly Dunaytsev in the quarterfinals. A few months later he won a silver medal in the light welterweight event of the 2014 Asian Games, taking three straight victories before losing to Wuttichai Masuk in the gold medal bout. Two judges scored the fight 28–28 while the third favored Masuk 29–27, giving the Thai veteran a rare split draw victory. In July 2015, Lim won two medals: a silver at the Golden Belt Tournament in Romania and a bronze at his second Chemistry Cup. He then reached the semi-finals of the 2015 Asian Championships, where he lost again to Masuk and took home the bronze medal. At the 2015 World Championships in Doha, he lost in the first round against Hovhannes Bachkov. In 2018 he won a bronze at the Beogradski Pobednik in Serbia before taking a quarter-finals exit at the Asian Games at the hands of eventual gold medalist Bobo-Usmon Baturov. The following year he lost to Masuk for a third time in his career in the finals of the Thailand Open International Tournament. He also took part in his second World Championships, beating Thulasi Tharumalingam before falling to Filip Wąchała.