I wouldn’t say the lives on the Lusitania really needed, or deserved, avenging, at the cost of an additional 320,518 American lives ended and maimed. The passengers took ship on a foreign vessel that was under credible threat of being sunk. They made their choice, and their foolish decision and the predictable result thereof was flimsy justification for the US jumping into the exact type of foreign entanglements that George Washington warned of. In my opinion, our involvement in WW1 directly led to terrible situation we as a nation find ourselves in today.
The Lusitania was a ship flagged by a belligerent, carrying contraband, and in a designated war zone. No sympathy for any American stupid enough to sail on it despite clear warnings from the Kaiser. There was nothing that the US would have been authorized in avenging.
The ship carried artillery fuses, guncotton, shrapnel for artillery shells, shells for 13 pound artillery, ready to fire but for the fuse. It is not clear whether the artillery shells and fuses caused the secondary explosion, and thus the sinking. (Official reports claim the shells and fuses were stored separately, which wasn't the usual practice).
The Lusitania was sunk because the Germans correctly ascertained that it was being used to ship arms, and the Germans even took out newspaper ads warning American civilians not to board her as it was being used to for the English war effort, and hence would be targeted as the non-neutral vessel that it was.