I always wondered,does a girl need to be someone I just met in order to have a relationship?

Absolutely not. In fact it's easier because you
1. have social proof - her from her past
2. comfort.
3. openers and conversation starters. "hey do you remember that time...?"

Now, if you have tried and been rejected in the past. You absolutely must NOT hit on her again. She will fall right back into that old thinking from before and the same thing will happen again. Instead you should intrigue her ect.. basic pick up.

If she liked you before and you were never interested you can try direct.

For real it is easier because you have a perfectly good excuse for talking to her. Catching up on old times. Just be fun and attractive and keep her moving around from one place to another with you if possible, it will bring her back to the thinking that you are a familiar face. Don't buy the into the thinking that women won't sleep with a good friend. If you are attractive to her she won't be thinking, he's my friend. She'll rationalize it that it's good that you know each other.

Anyway, she is just like any other girl except you have comfort and report in the bag already.

The only thing about women you already know is that they have already classified you. You might have to break her thinking patterns and prejudgements about you. Time usually resets things anyway.