"You can't do anything these days without upsetting someone," Mr Miller said.
"I didn't mean to upset the family. People asked whether I took their feelings into consideration, and I did.
"I had a long, hard think and I thought Mark would be happy to have the heat taken off him, to allow him to go shopping and go to the pub."
Mr Lundy was convicted in 2002 of murdering his wife, Christine, and their 7-year-old daughter, Amber, but had the convictions quashed by the Privy Council this month. He is now on bail and a court order prevents the publication of the name of the town where he is now living.
Mr Miller first suggested the Lundy Three Hundy event on Facebook on October 9. Since then the page for the event has reached more than 520 "likes" and seven teams from around the North Island have entered, with a further three expected to return their entry forms over the next day or so.
Mr Miller said he had always thought that Mark Lundy "was quite a marketable chap".
Feedback to the event has been mixed, with some criticising the poor taste of the race.
One Facebook user, Matt Comb, asked how Mr Miller would feel if the event was about his family being murdered.
"You have to be all levels of ugly to make fun of an event that resulted in the loss of human life. How hard it must be for the rest of the family involved that went through that horrific appeal," he wrote. "I know if my family had been murdered and someone thought it was fun to make a joke out of it, I would be devastated."
Mr Miller said participating teams of four to five people would have set tasks to accomplish.
Mr Lundy's lawyer, Malcolm Birdling, said his lawyers, family and supporters would not be making any comment.