Lyman is the narrator and protagonist, and typically the protagonist changes (the definition of dynamic) in response to the conflict of the story. In this story, however, Lyman remains a steady and relatively unchanging character, so he would best be classified as static.

The central conflict of the story emerges as Lyman tries to support his brother Henry after Henry's service as a Marine in the Vietnam War. Lyman proves to be fairly naïve about how the war might change his brother and simply looks forward to Henry's return, believing that they will pick up where they left off.

After three years of fighting in the war, Henry is forever changed when he returns home. He is withdrawn and jumpy, and Lyman is as steadfast as ever in trying to support his brother. This isn't a change, but the way he shows that he cares for Henry transforms because Henry has changed so much. Lyman begins watching out for Henry and tries to distract his mind by destroying their car so that Henry can work on fixing it back up.

In the end, Lyman isn't able to rescue Henry from his severe depression, and after sharing one final happy evening together, he watches his beloved brother take his own life. Lyman is a constant source of love and support for Henry, which points to an important message in this story. Sometimes people who are severely depressed cannot be rescued with the help of their loved ones alone—not even by those who love them the most and provide an unwavering sense of support.

First, we have to define what "static" and "dynamic" characters are.

A static character does not significantly change throughout the course of a story. Most commonly, these are supporting characters. A dynamic character changes, develops, or matures throughout a story. "Main" characters are usually dynamic.

With this being said, "The Red Convertible" leaves much of this open to interpretation. Even though Lyman is the narrator and protagonist, he does not show significant personal change or development throughout the bulk of story. He remains "stuck" in the ways of his life (and his love of the red convertible) while his brother, Henry, actually changes.

In the story, the red convertible symbolizes youth and naivety. Since he does not experience the Vietnam War like his brother does, Lyman embraces that naivety throughout the story, only letting it go at the very end. Henry, however, is incredibly dynamic, developing and changing drastically due to his time in Vietnam.

Overall, one could make the argument that Lyman is static or dynamic, depending on how you choose to interpret the end of the story when Lyman lets go of the convertible. He could be seen as dynamic since he does "let go" at the end, but he could also be viewed as static since we never really see how he personally changes after Henry's death.