Answer:
The First World War ended mainly due to the intervention of the American forces on the side of the Allies. The Americans can therefore be said to have won the war.
With the end of the war however, came the peace process and the same way Europe had relied on the Americans to end the war, they relied on them to negotiate a lasting peace.
However, there were still many unresolved issues and the central powers had not been completely defeated. Any peace was going to be very complicated as these issues needed to be dealt with.
This was why Harold Nicholson was wondering if the U.S. were going to be able to ensure a lasting peace the same way they had ended the war given the unresolved issues that remained.