Joe Lieberman called Amazon and said [something] to them.
Late that evening, Wikileaks was cut off.
The next day, Lieberman put out a press release: "This morning Amazon informed my staff that it has ceased to host the Wikileaks website. I wish that Amazon had taken this action earlier based on Wikileaks’ previous publication of classified material. The company’s decision to cut off Wikileaks now is the right decision and should set the standard for other companies Wikileaks is using to distribute its illegally seized material. I call on any other company or organization that is hosting Wikileaks to immediately terminate its relationship with them."
Lieberman's spokesperson added: "Senator Lieberman hopes that what has transpired with Amazon will send a message to other companies."
The next day, Lieberman introduced a bill in Congress that would make it a Federal crime to do what Amazon was doing, hosting the Wikileaks material.
You could characterize that as "pretty clear that Amazon didn't roll over because of Lieberman", but that characterization would be utterly mendacious.