Jack Twist's death was apparently listed as an accident by the original author because that is what Lureen was having to tell people. Lureen knew that Jack was gay. She says to the other woman at dinner that her husband never wanted to "dance" either meaning that he was not interested in her sexually. Lureen knew Jack was seeing a man named Ennis regularly. She also knew he would go out to meet other men for sex. She said to Ennis that she had told Jack not to "drink" (commit the act of homosexual sex). She says Jack "drank" often. She had tears in her eyes as she said these words.
She connected with Ennis in that moment because she knew this Ennis guy and Jack were wanting to be together but couldn't. She felt the same as Ennis: they each loved Jack but couldn't have him fully. Jack cheated on them both (with other men). They were each sad that Jack had died but also angry with him for cheating because he did not heed their warnings that being openly gay would get him killed. Obviously, Ennis was devastatingly saddened at perceptively knowing how Jack truly died. Lureen had to concoct a lie because of it. She told the lie to Ennis as she had stated it many times before to others, but she knew Ennis understood what had truly happened to Jack. He was brutally beaten to death.
Edit: I keep thinking this over! My first thought was that Jack committed suicide. But, after reading other people's theories, suicide didn't seem to fit. Second thought was that he was beaten to death. Could be. Could still be suicide. I don't think it is so important how Jack died but that he and Ennis never could find fulfillment.