The planned savings for the next year follow news of a projected overspend during this financial year of about £40m.
Much of that sum was down to the cost of children’s services and looked after children, with the children and families budget increasing by £12.8m since August.
The cost of adult social care also contributed to the overspend.
Lewis said those services were “hard to predict,” but the council had “plans in place” to try to better forecast how many people would need support.
He added that the overspend would be covered by the council’s reserves and contingency funding.
Lewis said that, like many residents, the council had seen rising costs for “energy, fuel for vehicles, things like that” and members were “trying to understand those costs and think about areas where we can reduce the cost of running the council”.
He said he had confidence that the government understood the challenges faced by councils and highlighted £20m the authority had received last year as a recovery grant to put back into services.
However, Alan Lamb, the leader of the Conservative group, the main opposition party on the council, said the authority seemed to have forgotten that it was there to “serve the people of Leeds”.
He said he expected the situation would “only get worse and people will keep seeing their bills go up and their services go down”.
“There is a better way to do it – we will set it out in our budget proposals. It doesn’t have to be like this,” he added.
The council is expected to publish its budget proposals, including how the savings will be made, in December.