While it's true that the U.S. did not declare war directly as a result of the sinking, it would be going too far (I think) to call it a myth, as that would suggest that it wasn't a factor. Germany's unrestricted submarine warfare was a massive reason for the U.S. entry into WWI. The Sinking of the Lusitania was inseparable from this policy. It was very much a stepping stone on the road to war.
Well, you can judge the truth of this fairly easily by looking at events.
May 7, 1915: The Lusitania is sunk by torpedo.
During 1915, the Germans sunk 1.3 million tons of merchant ships.
July 9, 1916: The unarmed 2,300 ton submarine Deutschland arrives in Baltimore on a trading mission.
Public domain photo.
November 1916: Deutschland arrives in New London, Connecticut for a second trading mission.
During 1916, the Germans sunk 2.3 million tons of merchant ships.
January 1917: A third trip is canceled. In February, Deutschland was fitted with six torpedo tubes and two 150mm canons. On March 28, 1917, it became U-155.
In January 1917, Germany's 150 divisions of troops faced 190 divisions. The British blockade was effective and Germany lacked enough surface strength to break it.
February 1, 1917: Unrestricted German U-boat warfare resumes.
February 3, 1917: The US breaks off diplomatic relations with Germany.
April 6, 1917: The US declares war.
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From this timeline, it is clear that the Lusitania did not precipitate the American entry into WWI (as I was told in high school). The US was still allowing German trading more than a year later. The precipitating event does seem to be the move back to unrestricted submarine warfare.