A. Wilson's administration knew at the time of her sailing that she had tons of munitions, aka contraband. That made her a legitimate target in a war zone.
Said knowledge was denied until the mid-1970's when a British underseas film crew released some of the photographs of her damage and cargo.
As if by magic the US government then "finds" her original cargo manifest. Seems the files had fallen behind a old file cabinet decades prior.
Imagine that. Imagine how many people knew. Imagine how that "secret" was kept for well over a half-century.
B. FDR was never "in charge" of the US Navy - that is, he was never Secretary of the Navy.
But, your question - think of the SS LUSTANIA as On-The-Job Training for FDR and WSC. And oh, what lessons they learned.
C. To this day the Admiralty has yet to release all of the SS LUSITANIA papers - coming up on a full century. See "Room 40"
Let's deal with this part first: Germans did officially provide fair warnings to passengers on the Lusatania:
"NOTICE!TRAVELLERS intending to embark on the Atlantic voyage
are reminded that a state of war exists between Germany and her allies and Great Britain and her allies; that the zone of war includes the waters adjacent to the British Isles; that, in accordance with formal notice given by the Imperial German Government, vessels flying the flag of Great Britain, or any of her allies, are liable to destruction in those waters and that travellers sailing in the war zone on the ships of Great Britain or her allies do so at their own risk.IMPERIAL GERMAN EMBASSY,
Washington, D.C. 22nd April 1915"
Second, what was the "contraband"?
Answer: some small arms ammunition, but this was not why Germans sank the Lusatania.
"She had aboard 4,200 cases of cartridges, but they were cartridges for small arms, packed in separate cases... they certainly do not come under the classification of ammunition. The United States authorities would not permit us to carry ammunition, classified as such by the military authorities, on a passenger liner. For years we have been sending small-arms cartridges abroad on the Lusitania.—New York Times, 10 May 1915[36]"
The reason for sinking the Lusatania, according to the German government was:
"The following day the German government issued an official communication regarding the sinking in which it said that the Cunard liner Lusitania "was yesterday torpedoed by a German submarine and sank", that the Lusitania "was naturally armed with guns, as were recently most of the English mercantile steamers" and that "as is well known here, she had large quantities of war material in her cargo".These charges were immediately denied:
"Dudley Field Malone, Collector of the Port of New York, issued an official denial to the German charges, saying that the Lusitania had been inspected before her departure and no guns were found, mounted or unmounted.And what has been found in recent dives?
Malone stated that no merchant ship would have been allowed to arm itself in the Port and leave the harbor.
Assistant Manager of the Cunard Line, Herman Winter, denied the charge that she carried munitions:"
"A dive team from Cork Sub Aqua Club, diving under license, discovered 15,000 rounds of the .303 (7.7×56mmR) caliber rifle ammunition transported on the Lusitania in boxes in the bow section of the ship.
The find was photographed but left in situ under the terms of the license.[68]
In December 2008, Gregg Bemis discovered a further four million rounds of .303 ammunition and announced plans to commission further dives in 2009 for a full-scale forensic examination of the wreck."
So, what exactly was it that "Wilson's administration knew at the time"?