No.

The Lusitania was sunk by the German boat U-20 commanded by Kapitänleutnant Walther Schwieger. According U-20's logs a single torpedo was fired at 14:10. The log also states that the ship's name, Lusitania, was clearly visible. Testimony of other crew members like Raimund Weisbach, are consistent with the official log. At the same time on the Lusitania the lookout, Leslie Morton, saw what he thought were two torpedoes and shouted a warning. Shortly after an explosion rocked the ship. The official version, that U-20 torpedoed the Lusitania is consistent with the testimonies of men on both ships.

A secondary question is if the British admiralty intentionally directed Lusitania toward a known danger in the hopes that it would be sunk. That seems unlikely as the admiralty was broadcasting information about known submarine dangers. On May 5th the Lusitania received warnings of submarines off of the south coast of Ireland. On May 7th, three hours before the sinking, they received this message, "U-boats active in southern part of Irish Channel. Last heard of twenty miles south of Coningbeg Light Vessel". An hour before the sinking they received, "Submarine five miles south of Cape Clear proceeding west when sighted at 10:00 am". This last warning was wrong there was no sub at Cape Clear.

So the admiralty was aware of U-20, and were attempting to locate and track it. They were providing merchants, including the Lusitania, the best intelligence they had at the time. That would be entirely counterproductive if they wanted the Germans to sink it. We know that Captain William Turner took those warnings seriously. He posted extra lookouts, had the watertight doors closed, and had the ship's boats partially prepped for quick launch if evacuation were necessary. In official inquests afterwards, there was a lot blame thrown around about what more he might have done. But if the Admiralty was trying to get it sunk, they were doing a terrible job.

Diana Preston's Wilful Murder. The Sinking of the Lusitania does a great job covering the sinking and the inquests.