Lu Bu = Greatest Warrior of China
Archilles = Greatest Legend of Greece
To begin ... let me rule just how “unbalanced” the fight will be ... heres the relative dates of the times of their appearences:
Lu Bu: 300 - 200 BC ish
Achilles = 1200-1000 BCE ish
So already as you can see, the Greeks and the West were beginning to emerge out from the Bronze age while the East were just about to begin advancing their weaponry beyond the Iron age. So we would be talking ... Bronze, early Iron swords/spears vs mastered iron, “refined” (I doubt steel) swords/spears ... hands down Lu Bu wins.
Should we ignore this fact and fuel the ongoing fued ... Lu bu and Achilles were both great warriors, to whom were amongst the best of their times, and a fist full of pride. But their abilities in battle are quite questioned. Archilles had a sence of honor, seeing as he did not willingly participate in the Trojan War until later. Lu bu, on the other hand, had no sence of honor what so ever as he cold bloodedly killed off Dong Zhuo. So should they meet in battle, Archilles would seek a way for a quick and swift extermination of his rival while Lu Bu would drag even the slightest stance into the total annihilation of his opposer. This most probuably would end up in a never ending fued where one man will strike the other only to be countered. More than likely, no actual victor will come out (as Lu Bu would more than likely exhaust himself and Achilles fear to proceed longer).
Should we even take the form of legend/myth into account, Achilles was considered a “god” while Lu Bu a warrior of great power. Even as Achilles may be “immortal”, his status of being so would mean he wouldn’t need to worry about the strength of Lu Bu and walk out into the feild in a bathrobe and killing him outright. But Lu bu was noted for his skills in archery, that of which could be notably beyond compared to that Paris. So if Achilles is a “god” and Lu Bu and master archer ... wouldnt Lu Bu kill Achilles seeing as Achilles would have no worry in the world (seeing as no armor/sheild would prove a major flaw as no man could match him in combat with spears/sword so why bother)? And don’t give me the “Oh, but he has armor." Ask any trained soldier or fighter; if they could lose the 30 pounds and deliever the damage and achieve the protection, they would. So why would Achilles bring armor than, if legend states he is as stunning as he is and as skilled?
Deny the fact if you may, but doing so would only lead to dismay. For the fact stands, Achilles is no “god”, he is man and must bear a sheild and armor in combat, thus relinquishing all possibilties of even the slightest chance that he was bore from deities. Lu Bu has his strengths, but as history showed he was a minor warlord, one of to whom could not possibly match many of the other “Kingdoms” generals. So I conclude, If the reality of the situation were to be brought in its full context, Lu Bu wins due to better technology and an pre-built agressive stance. Should you wish for a “Legendary” battle, chances are no person will win. Even as Lu Bu is an exelent archer, Achilles was no fool in combat.