“Mourning in Lod,” made by the Israeli director Hilla Medalia, was originally conceived as a documentary short about a murdered Israeli man whose kidney was donated to a Palestinian woman in East Jerusalem who would have died without the organ transplant. That feel-good story of grace and humanity amid the violence of the 2021 Israel-Palestine crisis is still on the surface of the potent, if scattershot, 71-minute feature that Medalia cut together in the end, but it’s almost completely overshadowed by the parallel — and far more ambivalent — story it tells about the value of personal charity in the face of systemic oppression.

The murdered Israeli was named Yigal Yehoshua, and by all accounts he was a kind and decent man who didn’t share his country’s genocidal animus towards his Palestinian neighbors. While driving through the “mixed” city of Lod one evening, Yehoshua was struck in the head by...