Tragedy can bring people closer 

Remember when the siblings met the Quagmires and they were one of the first friends that they ever made at the academy? I mean they all went through some serious loss with their families, so of course, they would grow close and want to help each other out.

Sometimes the kids are smarter than the adults 

Let's face it, most of the adults on the show were clueless about what was going on. The Baudelaires tried so many times to tell the adults that Count Olaf was nearby, but they were oblivious to that fact. So basically the lesson was is that sometimes kids are smarter than adults.

Trust your instincts 

Whenever they ended up in a situation, Violet often invented something to help her and her siblings out. She always trusted that the invention would work no matter what, and it always did. So if you ever doubt yourself trust yourself you can be right once in a while.

There is always a chance of redemption 

Remember Count Olaf's troupe? I was starting to think that there was some good in them and that they were basically just along for the ride. Especially the Hook-Handed Man Fernald. I knew he would eventually turn against Count Olaf when he helped Sunny and he found his sister. Also, the fact that his troupe was able to walk away when faced with peer pressure shows that you can stand up for what is right. They were also able to become actors in their own right without any help from Count Olaf.

As long as you have each other, you can do anything 

The Baudelaire's had faced a lot of trauma throughout the series. They always managed to get through it because they had each other. They had each other's skills to help them get through everything one common thing in every episode was the fact that with everything they faced they got closer with everything.