Not Your Average Daddy Warbucks
Jonathan Lyte, usually called Merchant Lyte or Mr. Lyte, is that rich old relative everybody wants to swoop in and save the day. He's Johnny's grandfather's elder brother, which makes him Johnny's granduncle or great-uncle (they mean the same thing). Instead of saving the day, of course, Merchant Lyte calls for the death penalty. Not cool, Daddy-O.
Merchant Lyte's major loves are money, his daughter Lavinia—those two deserve each other—and his shipping business. Technically a Tory, he's not above supporting the Whigs if he thinks it might line his pockets. "Lyte's crooked, you know" (4.2.25), says Rab to Johnny when he hears of the relationship. And he is. While Miss Lavinia claims he didn't mean to swindle Johnny and honestly wasn't aware of their relationship, we're not so sure—we don't trust Merchant Lyte as far as we can throw him.
So what's his function in the novel? He's a symbol, really, of Johnny's yearning toward his unknown family origins. His rejection of Johnny early in the novel is mirrored by Johnny's ultimate rejection of the Lyte connection when he burns the Lyte genealogy and leaves his own silver cup in the Lytes' country house.