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"?
Roosevelt had the original - a carbon copy actually, since the true original had gone down with the ship - bound in a leather case. Roosevelt was studying how a previous president, his mentor, had covered over his own route to war." A Time for War: Franklin Delano Roosevelt and the Path to Pearl Harbor, Robert Smith Thompson, Prentice-Hall Press, New York, NY, 1991, page 198.
" ... 4,200 cases of small-caliber rifle ammunition (amounting to 10-1/2 tons of explsoives), 1248 cases of shrapnel shells and 18 cases of fuses. ... was carrying even more munitions than this, that the ammunition in reality totaled six million rounds, and the 323 bales listed as raw furs were in fact a volatile type of gun cotton that exploded when brought into contact with water." American Heritage 'Seafarers Series' 'The U_Boats', Douglas Botting, editor, 1979, page 26.
Yup, the Imperial German Embassy, placed a NOTICE! "TRAVELLERS intending to embark on the Altantic voyage are reminded that a state of war exists between Germany and her allies and Great Britain and her allies; ..." This warning in fact appeared in the New York newspapers adjacent to the shipping schedule for CUNARD liners from May 1st to June 4th.
So ... the Wilson's administration knew at the time ... was her was carrying contraband.