I think the lessons are more for first-time public company CEOs that worked at one company for a long stretch of their career prior to becoming CEO.
Marissa Mayer spent her whole career at Google prior to accepting the Yahoo CEO position. Google, by anyone's standards, is a fantastic company with unbelievably strong people.
I worked at a similarly strong company in the 1990's - Maxim Integrated Products. Maxim, while certainly not as well-known as Google, was extremely successful. The company had a strong culture and a fantastic team of people.
When you work at a company like this for a long time (Eleven years in my case, Thirteen years in Mayer's case), you believe you can do just about anything. And you develop a strong belief that no matter what situation you are dropped into, you will come out victorious.
I know I felt that way when I left Maxim to implement a turnaround, and I wonder if Mayer felt that way when she left Google. I also wonder if she felt she could just implement Google's culture at Yahoo.
These were the lessons I learned:
A. Team matters!
Especially the quality of the team. You may be really good at what you do, but that doesn't matter because you need a strong team to work with. This leads to lesson number 2:
B. It's really, really hard to change a company culture.
And, it's even more difficult to change when the company has been struggling like Yahoo.
You don't fully appreciate how important a strong team and a great culture are until you experience working with a weak team in a shitty culture. To me, that's the lesson to learn.