Four Democratic House primaries in Illinois on Tuesday delivered mixed results for an array of super PACs tied to the American Israel Public Affairs Committee that spent more than $20 million to try to influence the outcomes. The pro-Israel lobbying group and its allies became a focal point in several closely watched contests in safely Democratic districts where the party’s nominees will be heavily favored in November. Two of the victors, Melissa Bean, a former U.S. representative, and Donna Miller, a Cook County commissioner, were buoyed by a barrage of cash from groups linked to AIPAC. But two other winners,...