What happened to Lucan remains a mystery and he was officially declared dead by the High Court in 1999.
Mr Bingham, who was in the house with his siblings at the time of the attack, said it was "extraordinarily unlikely" that his father was the killer or paid somebody else to carry out the atrocity.
"People will question my judgment. Others will dispute it," he said in an interview with the Daily Mirror.
"But what I am certain of is dad was not the prime mover in the situation.
"Weirdly, however, I do hope he was partly culpable because it makes me feel better."
The former merchant banker added that he would prefer that to trying to understand why his father had left the family for "no apparent reason".
Mr Bingham, 45, said: "I've always thought it extraordinarily unlikely my father went into our family home, wandered down and killed anybody with a piece of lead piping for the love of his children, while those very children might well have come downstairs and witnessed this appalling carnage."
He also dismissed the possibility of a contract killer being involved, but added he had no idea of the extent of his father's involvement or his guilt.
Following his disappearance, there were reported sightings of Lucan in Australia, Ireland and South Africa.
His brother Hugh Bingham said he was confident Lucan escaped the UK to begin a new life on the African continent.