I'm going to interpret this question as "What are some important lessons gained from studying history" rather than trying to enumerate some specific lessons from specific historical events. There are obviously more than the two I'm going to talk about here, but here's two that I find particularly valuable. Notably, they aren't lessons about history per se, but lessons that are good things for living in the world and they are gained by studying history in general.

First, I think that studying both highlights the importance of empathy and teaches us to be empathetic. When we study history we are studying people that are by definition different from ourselves. If we want to do those people justice and to really understand them and their history, there has to be a kind of empathetic affinity between the historian and the historical actor. Note that this doesn't necessarily mean that the relationship is sympathetic. You don't have to like the people you're studying. But if you want to understand them, empathy is an absolutely critical thing. I think this is actually one of the most critical features of reading primary sources because it much more easily facilitates that direct connection, particularly when you are reading hundreds and thousands of pages by a particular person or group of people. Good secondary literature can convey that too, but it's not easy.

Second, and on a totally different wavelength, is what I'll call "thinking historically" or in one word the importance of "historicity." Thinking historically demands that we contextualize; that we understand historical circumstance (which includes social, political, economic, cultural, circumstance). In other words, that we understand the concept of historical contingency. Historical contingency is that idea that things happen not because they were always bound to happen or couldn't be avoided (were inevitable), but that those things arise our of the broader historical circumstances. The value of this mode of thinking when thinking about history is, I hope, relatively clear. However, the lesson doesn't merely apply to studying things in the past. It is a critical idea for understanding the world as it is, not just because today's world came out of the past world, but because if we really want to understand things we have to push back against naturalizing and essentializing ideas (for example political doctrines), characteristics of peoples and cultures, structures of power, etc. Understanding all these things as contingent, I think, radically changes how you have to look at the world compared to when you assume things "just are" certain ways.