He said Independent had signed up more than 100 customers since beginning its sales push last month.
But the battle was not over yet, said Davidson, a former Lion managing director.
"What we're seeing is quite intense competitive responses from the other brewers, which is neat - that's what it's all about."
Davidson said DB had been giving discounts of up to $60 on its keg prices for on-premise operators that had been approached by Independent sales staff.
The wholesale price on a 25-litre keg of Independent-brewed Carlsberg was $130, he said, adding that consumers were unlikely to see any benefits from the discounting, as bar owners would probably just take bigger margins on sales.
"My question is - if [DB] are able to respond [to Independent's tap beer drive] with the level of price discounting that they have to date, why have they not been that competitive over the last 20 years?"
When asked about Davidson's claims, DB's Mark Campbell said the company did not comment on its arrangements with customers.
Davidson said he did not have any evidence of Lion discounting its tap beer, but the Newmarket-based company had been heavily discounting its ready-to-drink (RTD) alcoholic beverages as a way of "hurting" Independent's profitability. RTDs make up a large proportion of Independent's business.
"Putting very cheap prices in the market for RTDs seems like an unusual response to on-premise beer competition," Davidson said.
However, Lion's external affairs director, Liz Read, said pricing was "particularly competitive" at this time of the year.
"Beyond that it's business as usual and we're pricing based on our strategies in the marketplace," Read said. "We haven't done anything with our RTD prices."
Davidson said Independent had seen such high demand for its tap beer it was having to order more kegs from Europe.
"Our biggest challenge right now is making sure that we can manage the ramping up of supply with demand."
Independent liquor was founded in Auckland in 1987 by Michael Erceg, who died in a helicopter crash near Raglan in 2005. The company was acquired for $1.5 billion by Tokyo-listed Asahi, a Japanese brewer, in August.