Ruling Sword didn't rush to get into the Instance Dungeon. In other words, they always took their time to enter.
After Naxxramas had been opened up for a while, the other clubs had already brought their teams to attempt it. At the same time as they fought, they fixed up their team. If they needed any potions or other roles, they could address that later. Anyway, they had over a 100 elite players, so they could have three or five teams and it wouldn't be a problem.
The core of Lu Li's group was the three-way alliance's First Clear team. Although the rest also entered the Instance Dungeon, they didn't have much impact.
With the three-way-alliance's First Clear team, it didn't look like Drizzle Court and Peerless City had to worry.
However, it wasn't that there wasn't any hidden danger. If they took their time, their First Clear team would become weaker and weaker.
