Last year, Michael Rakowitz  got more attention for his protests than his participation in New York museums. He was the first artist to withdraw from the 2019 Whitney Biennial, providing a template for others whose departures eventually helped drive a tear-gas magnate from the museum’s board; later, in a move aimed at a board member of the Museum of Modern Art, Mr. Rakowitz tried to pause his own video work from a show at its sister institution, PS1.

Mr. Rakowitz’s current show at Lombard, at least, lets us assess his work on its own terms. Here the Chicago-based artist is showing the latest chapter in an ongoing project, “The Invisible Enemy Should Not Exist,” which reconstructs looted or destroyed Iraqi antiquities out of humble materials. An earlier exhibition focused on objects stolen from Baghdad’s National Museum; here, he and a team have remade reliefs of an Assyrian palace that was blasted by the Islamic State out of packets of mixed herbs, newspapers and other scraps from the regional economy.

I suppose the colorful reliefs have a baleful relevance for those of us already incensed by the cultural (and human) devastation of Iraq. But they are also rehearsed and self-contained, and that goes double for “The Ballad of Special Ops Cody,” a haughty work of stop-motion animation filmed at the Oriental Institute of the University of Chicago, which depicts a U.S. Army toy figurine inspecting the museum’s Near Eastern collection while a voice-over recounts various lootings and atrocities. Mr. Rakowitz is better when he pushes his historical and political engagement into generosity, as he did in his moving “Return,” his contested video at PS1, which allegorizes the Iraq war and refugee crisis through his red-tape-choked efforts to import Iraqi dates to Brooklyn.

This exhibition is Rakowitz’s fifth exhibition at Jane Lombard Gallery.

For the initial iteration of The invisible enemy should not exist, first shown at the former Lombard-Freid Gally in 2007, Rakowitz merged data from the University of Chicago’s Oriental Institute, UCLA, and Interpol, to recreate artifacts that were destroyed or looted from the National Museum of Iraq following the 2003 US invasion. Rakowitz crafted these artifacts out of Middle Eastern food packaging, Arabic newspapers, and other found media.

For this exhibition, Rakowitz presents reliefs from “Room F,” a banquet courtyard within King Ashurnasirpal II’s 9th century BC palace built in Kalhu, the ancient Assyrian city of Nimrud. By the time the palace was destroyed by ISIS in 2015, 400 of the 600 gypsum reliefs that once lined the walls had been removed by archeologists during expeditions and sent to museums in the West. In each iteration of The invisible enemy should not exist, Rakowitz and his studio team reappear the destroyed reliefs and replicate the architectural layout of the original rooms in which the panels were installed. The gaps between the reliefs reflect pieces that were extracted by the excavators, acknowledging the continued history of displacement in Iraq, creating what the artist calls a palimpsest of different moments of removal.

The Ballad of Special Ops Cody is on view alongside the reliefs. The stop-motion animation film centers around the unbelievable true story of an Iraqi insurgent group’s attempt to convince Americans that they had taken a soldier hostage. In 2005, photographs of the alleged captive held by gunpoint surfaced. The “hostage,” instead of being a captured soldier, was actually Special Ops Cody, a popular plastic doll sold on military bases. In the film, Rakowitz brings the action figure to life voiced by a veteran of the Iraq war. Cody is on a mission to liberate votive statues from their vitrines, but afraid and unsure they remained in the Oriental Institute where they lived on display. Rakowitz implores us to examine and honor these treasures while contemplating the human and cultural costs of the captive works we now see in museums.