The figure was revealed during a four-hour meeting yesterday, when controversial cabinet proposals to close more than 100 council buildings were under scrutiny.
Despite planned cuts, the county council had predicted a shortfall in its overall budget of £200m by 2021 and the mooted rise in council tax would reduce that amount by around £50m.
Deputy leader David Borrow said difficult decisions had to be made this week.
He said: “That amount is needed to get us anywhere near balancing the books.”
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But it still means the planned closures look set to go ahead.
Campaigners including Jane Porter and Alison Stevens attended the county hall meeting to hear what councillors had to say about the plans to close Fulwood Library.
Jane and the Help Save Fulwood Library group had collected more than 3,930 signatures on a protest petition against the planned closure.
Beforehand Jane was still optimistic the library could be saved and said her MP, Ben Wallace, was “monitoring the situation”.
Tory Coun Vivien Taylor asked what price the library could expect to be sold for and was told no valuations had been made.
She also challenged council leader County Coun Jenny Mein who said last week Fulwood library users would be able to get a bus into Preston to use the Harris Library instead, asking whether she would like to send children into town to complete homework tasks.
Tory councillors – angered they had been given days to analyse 1,000-page reports – failed in a bid to force a delay.