We get to see what happens to Henry Lamartine Jr. after he grows up… and it's not pretty. When we meet him as an adult, he has already been to Vietnam—and he's traumatized as a result.
We first get a glimpse of the adult Junior when he and Albertine meet up completely by chance in Fargo and land in bed together. It seems he's still suffering from some nasty PTSD when we/Albertine meet him; for example, when Albertine reaches over to touch him in his sleep, he freaks out.
Toward the end of the book, Lulu reflects on her son's downward spiral after the war, which apparently took her by surprise:
The one who went wild on me was unexpected. That was Henry Junior. All his life he did things right, and then the war showed him right was wrong. Something broke in him. His mind gave way. He was past all touch when he returned. (15.1.70)
Unsurprisingly, given the circumstances, Henry doesn't meet a happy end. A couple of years after his encounter with Albertine, he ends up drowning when he jumps into the river during an outing with his brother Lyman. Lyman pushes Henry's car into the river and tells everyone that they were in a car accident, presumably to protect everyone from the knowledge that Henry Jr. had (it seems) essentially committed suicide.