Lex was rather surprised. He was never interested in the king or royal family, so he didn't bother to look at how the whole throne system worked. That's why he was surprised that every third generation would inherit the throne.
This means that only the grandchildren of the king or queen will inherit the throne. This was surprising to him, who thought it was a generation-to-generation system.
"You guys look surprised," Amber smiled. But it's the truth. It's said that the second generation is usually spoiled and would ruin the kingdom. And guess what? Even after 400 years, we can see how stable and progressive our kingdom is."
Lex had to say Amber was right. However, many things were played out in Game of Thrones, such as the second generation manipulating the third generation.
One of the reasons he always stayed away from politics. He hated those manipulations and always kept a distance from manipulative people.