I'm late

In fact, I'm always be late.

"I'm always late for everything" would be a phrase we would use.

When I was a child, I believe it's very serious.thought it was very bad.

Run the two sentences together.

Of course, the teachers will would be angry if someone came late.

But nowadays, nobaody take keeps an eyes on me.

"Keep an eye on" means to watch carefully, like a parent or teacher would over a child.

I remenmber my grandpa told me what bad manners it was for youth young people to do everything late.

"I remember my grandpa told me what bad manners it was for young people to be late for everything" might be better.

I always put down what should i do.

That's fine -- you mean you write a list of everything you should do?

I don't want to do be a lazy girl like this.