It was most likely a conflation with “they shall not pass”, which the Wikipedia article notes:
was most famously used during the Battle of Verdun in World War I by French General Robert Nivelle. It appears on propaganda posters, such as that by Maurice Neumont after the Second Battle of the Marne, which was later adopted on uniform badges by units manning the Maginot Line. Later during the war, it also was used by Romanian soldiers during the Battle of Mărășești.
This opens the possibility that Tolkien himself was quite well aware of that form of the phrase and may have even been inspired by it.
It was also used during the Spanish Civil War and has since been used by various anti-fascist groups worldwide, as well as by the Sandinistas (according to the same Wikipedia article).
The timeline of it's usage, especially by the Sandinistas, makes it most likely that the conflation comes from the 60s counter-cultural movements, when their usage of it would have been well known and when popularity of LotR was really starting to take off (particularly in the US). Of course, someone who was around at the time would be needed to confirm that.