Honestly, though I would love to see it happen, especially to the grandest ship in history (Titanic), no shipwreck that has been under for an extended period of time, can be raised. Simply put, salt water is kryptonite to the steel that these large ocean liners are built mostly from.
However, unlike Titanic, both Britannic, and especially the Lusitania (unrelated, I know), are close enough to the surface that you could attempt to build a wall around them, then drain the interior of the wall and create an airtight vacuum chamber. This would prevent exterior humidity from deteriorating the ship any further.
From that point, far more extensive investigation of the ship can take place, and, due to the lack of moisture, the ship would last as long as the walls around her. While the cost of such an operation would still be obscene, it is far more feasible than trying to pull a buried, rapidly deteriorating, broken apart ship from the mud it has been stuck in for over 100 years.
One problem though: the metal's high salt content. I have no clue what to do about that. Any suggestions would be much appreciated.