The Graf Zeppelin was always planned to be filled with hydrogen, it was only after the R101 burned that Zeppelin began considering helium as a lifting gas. Had the Graf been filled with helium she would not have been able to make transAtlantic flights. Zeppelin even cancelled the planned LZ128 for the same reason and began work on the much bigger LZ129 Hindenburg which would have been viable with helium.
Zeppelin did not have formal negotiations with the American government about using helium in Hindenburg, instead relying on their chief Hugo Eckener's close friendship with Roosevelt to try and release the gas. However, the President's hands were tied by Congress passing the Helium Control Act which forbade the large scale export of the gas. Hindenburg was redesigned at a late stage as a hydrogen-inflated ship (she would have originally had two sets of gas cells, the main ones filled with helium for lift, the second filled with hydrogen acting as anti-ballast which would be vented to offset the loss in weight from burning fuel).
Hindenburg was inflated with hydrogen on her first season, Zeppelin were confident they could handle the gas safely - they had never had a hydrogen fire on any of their civilian ships - and the airship performed superbly. During the winter of 1936/37 she was laid up and her accommodation expanded to take advantage of the greater lift from hydrogen. She returned to the TransAtlantic route in the spring of 1937 and burned shortly afterwards.
It was only after the Lakehurst disaster that the Zeppelin company approached the US for an export license for helium to inflate Graf Zeppelin II - the Hindenburg's near twin. The ship had been redesigned to accommodate helium, including advanced water recovery systems that would reduce the need for venting gas. Once again Eckener appealed to Roosevelt and was given permission to have the gas. However, Harold Ickes blocked the export in retaliation for Germany's annexation of the Rhineland.
Graf Zeppelin II was inflated with hydrogen but never made a commercial flight, the US having blocked any hydrogen-filled ships from their territory. She spent a short life on propaganda missions for the Nazis and trying to ferret out the secrets of Britain's radar chain. The original Graf Zeppelin was deflated and turned into a museum. Both were scrapped early in World War 2.