Mr Jones said the email claimed "hundreds of thousands of dollars have been paid to both these entities in project payments".
"This is so that Lotto can sell tickets through the checkouts, worsening gambling spend at a time when Lotto bases itself on the myth of being the family concern. This was also because Countdown threatened to close Lotto counters in their stores."
Mr Jones did not say who the email was from.
Countdown last month began offering Lotto sales through its checkouts rather than at in-store counters.
A Countdown spokeswoman said: "Clearly this is a matter for the Lotteries Commission and they will address the comments raised."
Lotto NZ's Mr Pickup said it would be inappropriate for his organisation "to enter into a political debate".
"Suffice to say there is no substance to the allegations made, and we do not have any concerns of that nature. We have a good working relationship stretching back many years with our retailers, including Progressive Enterprises, and we look forward to these continuing."