The Dragon wants you to take out Lo Pan - hand to hand is a quest in Fallout 2.
Lo Pan and the Dragon are engaged in a struggle for the very soul of Shi-Town. The Chosen One can tip the balance in either one's favor by killing them. Working for the Dragon gives the people of Shi-Town hope, following the Dragon's selfless example.
After witnessing Lo Pan's defeat in a scripted cutscene after approaching the crossroads at the heart of Shi-Town, the player can talk to either leader to get their bearings. Lo Pan is much less discerning about how his rival is taken out. The player can talk to him in the gym to the northwest.
Dragon will explain his philosophy, wanting to share his knowledge of martial arts with all and blasting Lo Pan for being selfish. The player has to either have 125% Unarmed for Dragon to accept their offer of resolving the stalemate, or fight six of his men in a test of skill. If they do not have the requisite skill level, they can train with the Dragon for +5% to Unarmed. Defeating all six opponents nets 8000 experience points. Notably, the player can complete both challenges by not accepting either quest at first and completing both tests of skill. Thankfully, the player is healed automatically between fights.
Both ways lead to Dragon asking the player to take Lo Pan out in honorable combat. To challenge Lo Pan, the player either has to challenge him directly with 125% Unarmed or fight six of his men, before Lo Pan will enter the ring. Once knocked down to 33% health, Lo Pan will pull out a .223 pistol and use it to even the odds. After he's down, the player has to report to the Dragon for an additional 3000 experience points. Lo Pan's body cannot be looted.
Oddly enough, killing Lo Pan with super stimpaks is accepted by the Dragon as an honorable kill.
Behind the scenes
The Dragon is a reference to Bruce Lee, a martial arts master who starred in Robert Clouse's 1973 Enter the Dragon and Way/Return of the Dragon. In the latter, Lee ripped out Chuck Norris' chest hair out before killing him.
Lo Pan is named after the villain in the 1986 cult classic Big Trouble in Little China.