Casting lots occupies an unusual position: it is the one divinatory technique that appears in scripture with approval and is practised by the institutions that condemned the others.
The Hebrew Bible has land allotted by lot, duties assigned by lot, and the Urim and Thummim consulted for decisions, and the practice is presented as a way of removing human preference so that the outcome may be given rather than chosen. Early Christian narrative continues it: the replacement for Judas is selected by lot, and the account offers no apology for the method.
That precedent left the church in a difficult position. Divination in general was prohibited, yet the scriptural warrant for lots could not be argued away, and the compromise reached in practice was that lots were permissible when necessity was genuine and no personal advantage was sought, and forbidden as curiosity. The line was never stable. Opening a sacred book at random and reading the first verse found, a practice with its own name in Latin, was condemned by councils repeatedly and went on being used by people including bishops.
The underlying logic outlived the theology. Selection by lot was a central democratic mechanism in classical Athens, and its modern descendants, the jury drawn at random and the citizens' assembly, rest on the same idea: that where every candidate is acceptable, chance is the only selector that cannot be lobbied.
The technique is trivially simple, and its history is not.