Museum Piece is a Ray Boccino mission.
During the cutscene, Niko Bellic tells Ray to look for somebody he was hunting: Floran Cravic, while he was doing Ray's latest errand.
Ray's latest errand involves taking diamonds to the Libertonian, where a deal is going to occur to exchange Ray's diamonds for money. The peson wanting diamonds is Issac. After getting to the Libertonian, Niko meets Johnny Klebitz, a biker for The Lost, at the side entrance of the museum.
Inside, the deal doesn't go to plan as they are ambushed by Luis Fernando Lopez. Johnny runs off with the diamonds while Niko has to shoot his way out of the buiding. Outside, Niko steals one of the cars and has to shake off Issac's men before completing the mission.
Completing this mission unlocks Impossible Trinity, a reference to the fact that this is the only mission in the GTA IV storyline where all three Grand Theft Auto IV protagonists, Niko Bellic, Johnny Klebitz and Luis Fernando Lopez appear.