Great work RMF - I'm trying to look up Navajo beliefs about suicide, and I stumbled upon an interesting paper - unfortunately it is over 10 years old, but it referenced a couple of things that may reinforce the theory.
1. Of the suicides studied, the Navajo group had a male-to-female ratio of 9.8:1 vs. 4:1 nationally. It was noted that of those suicides studied, the researcher concluded that most of the suicides were impulsive (perhaps exacerbated by alcohol), so that is a point of difference I guess.
2. It was noted that since in Navajo belief it is very bad to see a dead body, most suicides happened away from the home. In some cases, the suicide was done in a place where an enemy could not help but find the body, and in that way the person would enact revenge. This would support Lyle's having traveled away to do this. He may have been intentionally misleading in order to ensure that his family would never ever know about his death but assume that he had cut times and was living off the reservation somewhere.
I hope that this line of inquiry is fruitful. It woud be nice to put Lyle to rest.