First of all, in which country will he sue you?
In which country you can find a law to sue people if Google hit your site?
This guy is just a big mouth guy.
He buy an adult site link or was a mistake?
If was a mistake, try to clean it. If he purchase and he thinks that those links was bad... it was his decision.
However, maybe he can go to Disneyland court and sue you or maybe in Secondlife court

Not in the real life.
Tell him that the article 399 bis of the Constitution says that no Gig purchased on fiverr.com can be sued he he
I saw you live in Brazil, he will go to Brazil to start a legal fight against you??? Brazil laws does not have juridistion on fiverr.com
You client sounds like a people that try to blame you for the Google crazy updates!!
But he sound very unmature, maybe he is only 13teen tears old, poor guy!!