The only way to bring a lawsuit is for an action to occur that triggers the suit. Otherwise, there is no breach of contract to sue over. If Parler believes they have a case against Amazon, they are able to file a lawsuit.

That said, Parler almost certainly has no case since private companies may do business with whomever they please and any terms in place almost certainly contain an at-will termination clause. Parler will need to find a new host and AWS will forfeit any future revenue from Parler. That’s an even exchange.