Sean D. Reyes , the attorney general of Utah, said in a statement that the state had “labored for decades to provide justice” for Mr. Lafferty’s victims.

“That the wheels of justice turn so slowly in cases like this is cruel and tragic,” Mr. Reyes said. “Now that Mr. Lafferty is facing his Maker, perhaps ultimate justice will be realized and there will finally be some closure for the family of the victims.”

The events leading to the killings began in 1983, when Mr. Lafferty was excommunicated from the Church of Jesus Christ of Latter-day Saints for his increasingly extreme religious views, according to court records. Those views included an embrace of polygamy, which the church banned in 1890.

Angered over his excommunication and the collapse of his marriage, Mr. Lafferty formed a breakaway polygamous sect with his brothers called the School of the Prophets in 1984. The brothers claimed they received messages from God.

Mr. Lafferty said one of those messages told him that his ex-wife, who had left him and taken their six children to Florida, had been the bride of Satan in a previous life.

In another message, he said, he was told that four people caused his excommunication and divorce, including his brother Allen’s wife, Brenda, and their 15-month-old daughter, Erica, “who he believed would grow up to be just as despicable as her mother,” according to court documents.

God told him to kill all four of them, Mr. Lafferty said. So on July 24, 1984 — a state holiday that commemorates the arrival of Mormons in the Salt Lake Valley — Mr. Lafferty and a group of followers, including his brother Daniel, went to Brenda’s house in American Fork, Utah.