Final answer:
The case that gave lower courts discretion in applying the test for qualified immunity is Pearson v. Callahan.
Step-by-step explanation:
In the case of Pearson v. Callahan, the Supreme Court gave lower courts some discretion over how they applied the test for qualified immunity. This 2009 decision allowed lower courts to decide, at their discretion, whether to follow the Saucier two-step sequence when dealing with qualified immunity, or to skip ahead to the core qualified immunity question if the case's particular circumstances warrant it. This flexibility aimed to streamline the legal process and lower the burden on courts dealing with qualified immunity issues. Pearson v. Callahan thus plays a significant role in shaping how courts address claims of qualified immunity.