The authority's chief executive, Phil Halsall, was suspended in August on full pay pending the outcome of a disciplinary investigation.
It followed an independent review of the tender process for a contract to run the council's fleet services.
Tim Kerr QC, a local government law specialist, is overseeing the probe.
He is examining council documents and interviewing members of staff and councillors.
Mr Halsall has denied any wrongdoing in the tendering process of the fleet contract.
The deal to run the council's fleet services was agreed in April by the former Conservative administration.
It was awarded to BT and One Connect Ltd, a partnership between BT and the council.
However, the decision to award the contract to BT in April was called in by county councillors and it was put on hold and the council's in-house provider continued to provide the services.
The contract was revoked on 15 August with immediate effect by the current leader of Lancashire County Council Jennifer Mein.
A senior lawyer has been appointed to carry out the investigation into a £5m tendering contract involving Lancashire County Council, it has emerged.