Lyle was a known outlaw and was eventually arrested for larceny in 1874. He died at some point later, which Arthur witnessed.
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.