The sinking of Lusitania didn't directly cause the United States to enter the war. It did, however, fuel virulent anti-German sentiment in Britain and the United States and hinder diplomatic relations between Germany and the United States
The problem was not that the Lusitania had been sunk but that American nationals were attacked by a foreign power. This cannot be excused in any situation. Woodrow Wilson was forced to act and hectare war on the triple alliance. I believe that an attack on America of any kind is considered a very serious issue and that the Wilson administration and the legislature reacted accordingly.