They got "Human-headed Winged Bull and Winged Lion (Lamassu), ca. 883–859 B.C. Northern Mesopotamian. Alabaster (gypsum). Gift of John D. Rockefeller Jr., 1932", but I do not think they went on display until much later.
The Met has built a special room on the second floor for these treasures. Around the walls of which are the large wall panels. I have a recollection that much after the British Museum put their panels on display someone was doing a thesis on how the British Museum got the panels. This led to a school in England where the additional panels (now at the Met) were thought to be mere copies of what went to the British Museum. But it turned out that they were half of the original amount and not copies. The Met bought them and built the very large display space.
That new display room MUST be quite recent ! I can tell you, catagorically,and as an eyewitness, first hand, that these staues and wall panels were NOT on display from the 1940s through 1990 or so ! At one time, I knew every inch of public display in the Met. LOL
The vast majority of the Cloisters' collection ( as well as the land ) is from the donations of the Rockefellers too. If it weren't for them, much of this unreplaceable art work, would NOT be in N.Y.C. !
Many thanks for posting all of this neat info. I guess that a trip to the Met, by me, is called for. :-)