Jesse, one can hold too all the reasons they want to on this, but it really doesn't change anything. While I wouldn't put it past the Admiralty to engage in a cover up, it would have been ex post facto to the sinking itself and done in order to hide their own mistakes. I don't think any competant historian would claim they didn't make any, and screwups such as what lead to the loss of a liner to enemy action are not the sort of thing you advertise to "The Peepuhl" during war.
A conspiracy to get a specific ship sunk doesn't really work well because there would be one actor in the drama who would have no reason to play along, and who's actions could not be anticipated much less planned for, and that would be the skipper of the U-20. (Unless somebody can show evidence that he met with the First Sea Lord to arrange all this. In the middle of a bitter war, that one's going to be a tough pill to swallow.)
Grand conspiracy theories thrive in the wake of extrodinary events, usually in an attempt to make some sense of them. They rarely hold up under close scrutiny when the selective thinking that goes into it all is exposed for what it is, and in the case of the Lusitania, there's really no need to look for the extrodinary when the ship was the victim of the mundane.
Lusitania sailed into a war zone.
Lusitania was spotted by a hostile submarine.
Lusitania was identified as a ship belonging to a belligerant.
Lusitania made a turn towards the hostile submarine which made it possible for the submarine to get a good firing solution.
Lusitania was torpedoed.
Lusitania sank as a result of being torpedoed. (Ships that eat explosives tend to do that)
A lot of people died.
An all too understandable sequence of cause and effect where Lusitania had a very bad day, and U-20 had a very good one. Tragic to be sure, but that's how war works.