There are many conflicting reports that the German U-20 didn't realise it was the
Lusitania until after the torpedo had been fired.
When the skipper of the U-20 Walther Schwieger ordered a check on the vessel, someone called back that it was either the 'Lusitania or Mauretania, both are armed cruisers used for trooping.'
Another report is that one man didn't realise it was the Lusitania until he looked through the periscope and saw the name written in gold on the stern. At that point, he was heard to remark 'Mein Gott! It's the Lusitania'. The name on the stern however was painted over, the couldn't possibly have been able to see it.
Another thing is that a German U boat waited outside Liverpool for the Lusitania in March of 1915 - 2 months before she was sunk.
Finally, the Lusitania was, in my opinion, carrying a certain amount of ammunition destined for Britain from America. We can take this into account as a reason for the sinking, but with 1,959 civilians aboard, is it really worth the risk of killing them?
Many ships have survived torpedo attacks.
Carpathia sank with three slamming into her side. Justicia went down after about 7 hits. Lusitania was an English ship, and would appear large enough to survive one torpedo and evacuate the people aboard before sinking her.
Lusitania was an unfortunate victim of war. Used for propaganda on both sides, she fueled hatred between Britain and the German Empire, and while in my mind, the German U-Boat had no right to sink it, the people aboard were given sufficient warning before going aboard.