Short answer: The God of War title was not about who was the greatest warrior of the three kingdoms, Lu Bu wasn't seen as the greatest warrior and his personal failings would have gone against him, Guan Yu's reputation for honour (and perhaps a degree of fortune he died in Jing where local worship happened) built and there were shrines to him that grew, as Shu became more popular in the troubles that came after the three kingdoms and religions tapped into his Jing popularity, Guan Yu's legend grew.
Longer answer: Was Lu Bu the greatest warrior of the three kingdoms era? He was an exceptional warrior, of great strength, bravery, highly skilled in horsemanship and archery, he was a famed as a warrior. He is said to have won a duel against Guo Si according to contemporary source Wang Can, his archery feat in negotiations between Ji Ling and Liu Bei to settle a war drew admiration from all around.
He would be a candidate but the records don't go as far as calling him the greatest warrior. That best warrior image more comes from the novel romance of the three kingdoms where he duels the three brothers at the fictional battle of Huluo Gate or Wei needing to 7-1 him, the novel also really goes negatively for his character particularly in his final chapter
The problem is Lu Bu was not worshipped by people, selecting him was not building on a base of support and even getting around that, Lu Bu might not be someone one wishes to highlight. He was a man of many flaws and while bullying, womanizing, bad decision making might be ignored, his killing two of his lords, including one (Dong Zhuo) of which he had taken an oath of father and son so adding a most unfilial act, and by his end, he had allied then turned against his local rivals around Xu (in no particular order Cao Cao, Yuan Shu, Liu Bei, even Zang Ba's Taishan group) at various points.
With the importance of loyalty and filial piety, a father killing renowned backstabbed does not set a great example. If this is the man your seeking to deify, what signal does it sound about you and what signal does it send about issues of loyalty?
Guan Yu was, like Lu Bu, seen as a great warrior, appraised by Wei official Cheng Yu as (along with Zhang Fei) worth ten thousand men. He killed the Yuan general Yan Liang in a daring raid in the midst of Yan Liang's army, there is the arm operation to have bone scrapped while at a banquet with his officers. He was held in high regard by rival officers like the warlord Cao Cao, the Wu generals Zhou Yu and Lu Meng, he was soon worshipped (along with the scholar warlord Liu Biao) in Jing. He also had his flaws, he was arrogant towards scholar-officials under him and accused by Chen Shou of being boastful, elements that played their part in his fall but nothing as bad as Lu Bu, no adopted father killing for example.
Indeed Guan Yu had a reputation for honour and loyalty. Having been separated from his lord Liu Bei after their revolt in Xu against Cao Cao, he ended up under Cao Cao and Liu Bei under Cao Cao's rival Yuan Shao. Guan Yu was treated well and given rank, when he killed Yan Liang he was enfeoffed but it became clear to Cao Cao that Guan Yu wished to return to his close friend.
Guan Yu had felt he repaid his debt by killing Yan Liang and when he left, returned the many gifts Cao Cao had given him so Cao Cao ordered no pursuit. Guan Yu had left wealth and rank under a powerful lord to serve an old friend whose future was unclear and who was forced to serve others with no guarantee of reward. This sort of behaviour was rather better to highlight and showcase than a twice lord killer. It is that sense of him as a man of honour that became important.
Guan Yu's reputation growth in fiction
As Jin collapsed and invasion from the north became a problem, discussions about had legitimately succeeded Emperor Xian began, some backed Han-Wei-Jin, others saw Liu Bei as a man of the Han line as the one to inherit the mandate. Nostalgia for the stability of the Han vs times of chaos, loving of that a sandal seller rose to be an Emperor, fighting through adversity against the larger power of Cao Cao with Liu Bei's "brothers" meant tales of their adventures against Cao Cao became popular.
Over time the tales had grown with works like the Records of the Three Kingdoms in Plain Language pushing his being a holy figure, a righteous protector. Guan Yu would also be a figure most dynasties seem to have been able to accept, to try to tap into his growing legend without any awkwardness for their own claims. Plays about the three kingdoms were popular by the Yuan dynasty and with them, more and more tales of Guan Yu's honour like letting Cao Cao pass at Huarong pass or his being a refugee from slaying a corrupt figure when he first meets Liu Bei came into being. Guan Yu also became not a general of a warlord faction in a civil war but a General of the Han itself.
Tales like The Story of Hua Guan Suo introduced a fictional son in Guan Suo and turned the already existing creation of Zhou Cang into a Guan Yu loyalist, both furthering the legend of Guan Yu. The Yuan work Records of the Three Kingdoms in Plain Language even has Guan Yu ascending into the heavens. The famed novel Romance of the three kingdoms more than happily played into these particularly when Guan Yu dies, his spirit avenging his own death and helping monks
Lu Bu was just a warlord who dies early. A mighty warrior but a failed warlord who didn't tap into such narratives to become a hero and in the romance of the three kingdoms, while he isn't a tyrant or the worst figure, his moral character is torn into and made worse. He is weak, disloyal, double unfilial, dishonourable, listens to his wives on military matters (the novel really didn't like him doing that), a coward in the end.
Religion
I have mentioned worship and after the 3kingdoms ended, Guan Yu over time became a worshipped figure anyway in Jing (which had a belief in worshipping local notables), said to have appeared in battles in Jing during the sixth century. In the early days, some of it was fear of a general who died in battle and had his head sent to Cao Cao while his body remained in Jing, making offerings to keep him vengeance but over time that changed.
A shrine at Yuquan Mountain was set up during the Six Dynasty periods for Guan Yu and it became linked with a nearby Buddhist Temple that Guan Yu was said to have helped create in the Tang dynasty. Buddhists incorporated the local deity Guan Yu into their local teachings, claiming he became vegetarian due to their teachings and his popularity spread as they spread word of his monastery protecting ways.
Taoists were initially against Guan Yu for his failings and preferred figures like Pang De but with Guan Yu rising status among the Buddhists, the Taoists added him to their pantheon over time. During the times of the Southern Song the ghost of Guan Yu was said to help the Celestial Master against a dragon (then later changed to Chiyou) in his home area and he became used in rituals to banish demons.
Guan Yu was building a reputation for protecting monasteries and temples, miracles attributed to him and religions happy to tap into a pre-existing worshipped figure. Initially, imperial courts like the Tang tended to treat him as a heroic general who had died for the state so got worshipped on that level rather than the localized worship as a deity but it grew over time and the Song dynasty formerly elevated him to deity status and his worship grew even further with more temples popping up over time, the Ming dynasty made him a God of War for his valour and loyalty.
Lu Bu never seems to have been worshipped in Xu, he had lived there for only three or so years and they did not have that same local worship as far as I have seen. Guan Yu had been in Jing for around 19 years and it was a province that had it owns local beliefs which Guan Yu's long service there and death played into. With that preexisting, other beliefs would tap into it and help spread his legend further, Lu Bu never had that.
I hope this helps and you have a good weekend
Sources:
Various SGZ by Chen Shou (Zhang Fei, Guan Yu, Lu Bu) translated by Yang Zhengyuan
Imperial Warlord and Generals of South by Rafe De Crespigny
Guan Yu’s life after death: The religious and literary images of the Three Kingdoms hero Guan Yu by Jesper Timmerman
Making the Guan Yu cult: The Rise of National Sacrifice, Buddhism and Taoism by Li Teng