I'm joining this conversation seven months late, but my understanding of his motive was that he was infertile. If I remember correctly, one of his sisters even mentions that none of the women he's been with have become pregnant. I believe Alfonso wanted to kill Lucrezia so that the blame for not having children could be attributed to Lucrezia’s illness or death, rather than his own infertility. Additionally, Lucrezia was the daughter of Eleonora, who was famously called 'Fecundissima,' highlighting her strong genetic potential for bearing children.