In the history of Zhengshi, Sun Quan did not tell Lü Meng not to kill Guan Yu, and even in Sun Quan's view, Guan Yu had to kill. You must know that Lü Meng is only a general, and if he catches Guan Yu, he will certainly not dare to make a decision easily. After all, this person was Liu Bei's good brother and the first general of the Shu Han Dynasty.
If such a person were killed without authorization, it would inevitably lead to a rupture between Eastern Wu and Shu Han. Therefore, before killing Guan Yu, Lü Meng would definitely have consulted with Sun Quan.
Lü Meng's killing of Guan Yu was authorized by Sun Quan.
Even before they fought, they had agreed that they must kill Guan Yu.

Why?
You must know that at this time, Sun Quan has clearly understood Liu Bei's ambitions, Liu Bei's momentum and his actions are to unify the world. Originally, Liu Bei and Sun Quan were allies, and they fought against Cao Cao together.
However, in the future, Liu Bei did a lot of things that made Sun Quan feel unhappy, and he felt that Liu Bei as a person must be killed, or to weaken Liu Bei's power.
Let's give a few examples:
1. After the Battle of Chibi, Cao Cao suffered a defeat, and at this time Cao Cao did not dare to easily launch a war with Liu Bei and Sun Quan. Sun Quan found Liu Bei and said, Let's join forces to take down the Shu kingdom.
However, Liu Bei did not agree, he told Sun Quan that he planned to recuperate recently, after all, after fighting for so many years, it was time to rest and rest.
Originally, Sun Quan's soldiers were all sent out, but Liu Bei told him not to fight.
Sun Quan could only retreat.
However, after Sun Quan withdrew, Liu Bei himself took his troops to attack the State of Shu, and Liu Bei also attacked the State of Shu.
This shows that Liu Bei wants to strengthen his strength, and he is not willing to play with Sun Quan.
Liu Bei occupied jingzhou and Yizhou, and his strength made Sun Quan feel afraid.
2. After Liu Bei occupied Shudi, the first thing he did was to fight Hanzhong.
At this time, Hanzhong was in Cao Cao's hands. Obviously, Liu Bei's intentions were obvious, he was following Liu Bang's example and wanting to occupy the Shu state, and then continued to attack Hanzhong. As long as Hanzhong is occupied, they can send troops to Guanzhong.
At that time, Liu Bang was under the leadership of Han Xin, from Hanzhong to Guanzhong, and then chased the deer to the Central Plains and unified the world. Liu Bei also wanted to follow Liu Bang's old path.
He wanted to unify the world, not only to destroy Cao Cao, but also to destroy Sun Quan.
Sun Quan saw Liu Bei's ambitions, so he wanted to turn Liu Bei against him.
Even when Liu Bei attacked Hanzhong, Guan Yu, who was guarding Jingzhou, could not sit still. He himself took his troops to the north of Jingzhou and went to fight with Cao Cao.
This is also the historical Battle of Xiangfan.
In Guan Yu's view, his approach was to disperse Cao Cao's forces and reduce the resistance of Liu Bei's attack.
Originally, Guan Yu was guarding Jingzhou and wanted to defend Eastern Wu. At this time, he took his troops away to attack Cao Cao, and Sun Quan saw the opportunity to defeat Guan Yu.
Because Guan Yu's rear was empty.
Sun Quan then wrote to Cao Cao, saying that the two of them had jointly killed Guan Yu. Cao Cao couldn't ask for it, because Cao Cao didn't know how to relieve the siege of Xiangfan?
Guan Yu was attacked from the rear by the army of Lü Meng and Lu Xun sent by Sun Quan, and Guan Yu, who was about to win the battle, finally fought a defeat and had to flee.
It was when he escaped that he was caught by Lü Meng's men, and then it was lü Meng who eventually killed Guan Yu.
Guan Yu was dead, and for Sun Quan, he no longer had to fear Liu Bei. Because this place in Jingzhou, from Liu Bei's territory, became Sun Quan's territory.
Sun Quan's strength has grown a lot.
Liu Bei only had one Shu state left, and he could no longer turn over the wind and waves.
More critically, Guan Yu's death was tantamount to breaking Liu Bei's arm. Therefore, Liu Bei is no longer Sun Quan's opponent, and this is what Sun Quan wants to see.
Therefore, killing Guan Yu was by no means Lü Meng's private message, but to cripple Liu Bei, leaving him with no foothold, at least not the possibility of hegemony.
Guan Yu must die, and the opportunity must not be lost and not come again. Facts have proved that Lü Meng's killing of Guan Yu was a correct decision.