The row broke out at a meeting of the authority’s cabinet which heard that a legal challenge by two NHS trusts to the awarding of a contract to Virgin Care would probably cost the public purse more than Â£250,000.
It also later emerged that the county council is to pay 75 percent of the total legal bill - expected to be in the region of Â£200,000 - with the NHS contributing the remainder.
The trusts which currently deliver the healthy child programme - which includes immunisation and screening services for the county’s youngsters - took the council to court following its decision to move to the private healthcare firm late last year.
The authority was found to have conducted the procurement process properly overall, but was ordered to re-run the final stage, because of concerns over how it had evaluated the two applications.
However, the same conclusion was reached after the tenders were reconsidered - with Lancashire Care NHS Trust and Blackpool Teaching Hospitals once again losing out to Virgin last month.
Leader of the Conservative-run authority, Geoff Driver, accused the previous Labour administration of inviting private sector bidders in the first place.
“You made the decision to go out to tender - you were given an option of keeping [the contract] in-house and you chose not to,” County Cllr Driver said.
“After you made that decision in February 2017, it was a matter for officers to deal with - not elected members - and officers implemented the decision that you had taken.
“If we’d have been in your position, we’d have kept the service in-house,” he added.
But Labour opposition group leader Azhar Ali said that he had been advised at the time that a number of services had to be offered to the market.
"But the assessment...was done under a Conservative administration - it was under you that the service has ended up being privatised,” County Cllr Ali said.
“You can come out with all the hype you believe in, but the public and NHS staff know that it was a Geoff Driver administration that made this decision and cocked it up.”
The meeting heard that the bids were assessed on the basis of quality and cost - but that price accounted for just 20 percent of the value attached to each tender.
Cabinet member for health, Shaun Turner, told the meeting that there was “a marked difference” between the quality of the two applications.
After the courts ordered that the final moderation process should be repeated, the council appointed a new panel of independent experts - chaired by a senior QC and including former executive directors from within the NHS and local government. They averaged out the scores awarded to each of the bidders across all of the relevant criteria and concluded that Virgin Care came out on top.
In a statement after the meeting, Lancashire Care NHS Trust, speaking for the first time since a legal ‘standstill’ period ended, said it was “disappointed”: A spokesperson added:
“There was a very narrow margin between the scores and we believe that this service is best placed within the local NHS which has a track record of delivery and the interface with other teams that also play a vital role in the provision of health services for children in their early years and beyond.
“Our previous procurement law challenges was successful, with the court finding deficiencies in the process.
"Whilst we are disappointed, we accept this outcome and will continue to work alongside Lancashire County Council as a core partner in the Integrated Care System for Lancashire and South Cumbria.”
The total legal costs in the case are still being finalised.