Lyman Lamartine is very much a static character in that he doesn't really change throughout the story. In narrative terms, this shouldn't come as a surprise, as Lyman is there to provide some stability in the story in contrast to the changing personality of his brother, Henry.
It's not just the story that needs Lyman to be static; Henry needs this, too. Lyman cannot really be there for his brother and can't really help him deal with his emotional and psychological problems if he isn't relatively stable and unchanging. He has to be the still point in Henry's turning world, as there's virtually nothing else in Henry's life that can possibly fit the bill.
As it transpires, Henry is beyond hope, and there's absolutely nothing that Lyman or anyone else can do to save him. There is, therefore, a tragic sense of inevitability about his untimely death. The sad truth is that Henry is just too far gone due to his traumatic experiences from serving in Vietnam.
But of course, Lyman doesn't know this;...
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