Lucas could tell clearly that the Brookes were only agreeing to submit to him on the surface, but in reality, they were just out to use his influence and power to strengthen themselves.
In fact, it wasn't difficult to guess their mindset. They merely thought that Lucas's current ability was not enough for him to compete with a big family like the Huttons.
In their eyes, the Stardust Corporation was merely doing well in Orange County because of the prestige of the Huttons. Once Lucas chose to go against the Huttons in the future, he wouldn't have the slightest advantage or chance of winning at all. They felt that he was just being delusional by thinking that he could win against a family that was far stronger than him.
Lucas's other identity could not be easily exposed, so there was no way he could use it as deterrence either.