Beckingham faces seven charges of manslaughter following an outbreak of Legionnaires' disease at the Forum 28 arts centre in Barrow.
She had previously been found guilty of the charges at Preston Crown Court, but won the right to a retrial at the beginning of this year.
In the first trial, the court heard that Beckingham was so negligent in her failure to maintain an air-conditioning system that she caused the deaths of seven people in July 2002.
The incident was the worst ever outbreak of legionnaires' disease in Britain, killing six women and one man and infecting nearly 200 other people.
Beckingham was the council's head of design services at the time.
Alistair Webster QC, prosecuting, told the jury in the original trial that the deaths were 'avoidable and unnecessary'.
'It was an outbreak that could have been avoided by the exercise of a moderate amount of care,' he told the court.
'The person who was properly responsible for this human disaster was Gillian Beckingham'.
Webster told the court that Beckingham, 45, 'failed to take any effective action' to prevent the tragedy. '[The] outbreak was caused by negligence so gross it was criminal'.