Mr Lee said the council needed to come to grips with what he believed was a "monumental financial scandal" that could cost tens of millions, if not hundreds of millions, of dollars.
"I think we are being taken to the cleaners," he said.
In May, the Herald reported that the cost of building city computer systems over the next eight years was $506 million - $56 million already spent, $150 million of budgeted spending and $300 million of unbudgeted spending.
At the time, Mayor Len Brown said the extra spending would be subject to "intense scrutiny" before being approved.
Yesterday, the acting chairman of the strategy and finance committee, Des Morrison, tried to push through the vote on the extra $7 million without any debate after four minutes.
Only two days earlier, the Citizens & Ratepayers member was one of nine councillors who voted against spending a further $1.5 million on the Rugby World Cup after nearly three hours of heated debate.
Councillor George Wood said Mr Lee raised some serious issues that the committee could not walk away from, and tabled an amendment asking for a report on why the former regional council computer system now used by Auckland Transport was not modified for the Auckland Council.
Mr Morrison and two other C&R councillors, Noelene Raffills and Dick Quax, voted against the amendment. It was passed by 12 votes to five.
Mr McKenzie said the decision to build the $54 million system was made by the Auckland Transition Agency.
Professional experts had advised the agency not to use existing systems, and that advice had been independently reviewed and confirmed.
"We have to play the game that is in front of us and that is to make the best use of technology to help us run our business as effectively and efficiently as possible," Mr McKenzie said.
A report to councillors said the $7 million for the procurement and purchasing improvements project was expected to result in cost savings of between $13.4 million and $18.5 million over nine years.
In May, councillors were advised of a $70 million IT investment programme this financial year whichdid not include any spending forprocurement and purchasing improvements on the $54 million computer system.
System error
* $54m Cost of new Super City system.
* $7m Extra needed to get it up to scratch.
* $2.2m Cost of using old system to do same job.