The type of law that would fail the Lemon test is:
a law that does not have a secular purpose
The Lemon test, established in the Supreme Court case Lemon v. Kurtzman (1971), is used to determine whether a law violates the Establishment Clause of the First Amendment. The test includes three criteria: (1) the law must have a secular purpose, (2) it must not primarily advance or inhibit religion, and (3) it must not result in excessive entanglement with religion. If a law does not have a secular purpose, it would fail the Lemon test.