Lyle was a known outlaw and was eventually arrested for larceny in 1874. At some point he died; Arthur witnessed his death.
Not much is known about the relationship between Lyle and his son, though the little information given implies a strained one at best. In regards to his death, Arthur says "it weren't soon enough," and refers to him as a "no good bastard" in a journal entry after his tuberculosis diagnosis. Despite this, Arthur keeps a picture of him next to his bed over two decades later and also wears his hat, hinting at some measure of fondness.