Rodman Ward is basically the Swinging '70s in human form. Though that sounds pretty cool to us, Lyman is far less fond of his son's freewheeling views.
To put it simply, Rodman represents everything that Lyman hates about the current generation. He believes in radical leftist politics. He studies, gasp, sociology instead of history. And, most importantly, he thinks that he knows everything, that he has the perfect solution for every problem that plagues the world. To Lyman, this is evidence of his son's supreme lack of maturity.
But, we think that Lyman is giving Rodman (who comes up with the names in this family?) short shrift. It's obvious to us that Rodman adores his dad, even if he shows that love in a ham-fisted way. What's more, he also cares a great deal about his mom, telling Lyman that "she doesn't look good" in an attempt to get them to reconnect (4.1.73). Rodman knows that his parents need each other, even if they're both too proud to admit it.
We're not totally sure what the future holds in store for Lyman and Rodman's relationship. While we doubt that the two men will become best buds anytime soon, we're confident that their experiences over the course of the novel will leave their bond stronger than ever before.