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.
Whether the sinking of the Lusitania can be considered an act of war depends on perspective. For instance, against Britain, the sinking was definitely an act of war. Britain and Germany were opposing participants in WWI, and Lusitania was a British liner sunken by a German submarine. German submarines were engaging in immense warfare during this time, torpedoing any enemy ships they saw and killing thousands. While attacking unarmed ships was permitted, submarines had to emerge from the water, announce their attack, and secure the survival of those onboard. Germany did not abide by these rules.
When the sinking of the Lusitania is brought up, most people associate it with being a big factor provoking the United States to enter the war in 1917. In the case of America though, I'm not sure I would consider the attack an act of war. For one, even though Americans died, the Lusitania was a British ship, so the target was not actually America. Also indicative that the sinking was not an act of war against Americans was the response afterwards. About a year after, in May of 1916, the Germans issued the Sussex pledge, agreeing not to sink merchant ships without informing them first, and providing for safety.
As the question is kind of an opinion, I thought it might be good to look up the definition of act of war, so I provided a link below. Hope it helps!