The answer to this is, in many ways, a matter of opinion. My own view is that the sinking of the Lusitania was not an act of war against the United States. If it had been a clear-cut act of war against the US, it is likely that the US would have entered the war against Germany immediately.
The reason that I say this was not an act of war is that it was not a clear and unprovoked attack against Americans. There are a number of reasons for this. First, the Lusitania was not an American ship. It was a British ship and Britain was at war with Germany. Second, the ship was carrying war materials even though it was not supposed to be. These two facts make it a legitimate military target. Third, the Germans had declared the waters around the British Isles to be a war zone. In other words, they had given warning that people should not travel in that area. Finally, it is not clear that the Germans should have known that there were Americans on the liner.
All of this combines to make this something less than a clear and unprovoked attack on Americans. Therefore, I do not see this as an act of war.