Lu Li had underestimated Ling Feidu's status in the Cabinet of Cloud and was unaware of the fact that Ling Feidu's grandpa was one of the three founding members.
Even if it were Lou Shi'er that murdered Ling Feidu when there was conclusive evidence and consent from Chief of the Cabinet of Cloud, the Pavilion of Misty Drizzle would not be able to protect Lou Shi'er.
There was competition, cooperation, disputes and as well as feelings of gratitude or resentment among the 72 sects. On top of all those, there was bottom lines and basic rules. The principle was that regardless of any conflicts or disputes, the important disciples could not be killed.
Once that principle was violated, the two sects could turn hostile against each other. When two major sects were at war, nobody could afford to suffer the loss.
Killing Ling Feidu was a violation of the principle.