The tech giant HPE won a UK High Court civil claim against Dr Lynch in 2022, accusing him and his former finance director, Sushovan Hussain, of fraud over its 11 billion dollar (£8.37bn) takeover of his software company Autonomy in 2011.
In June this year, Dr Lynch was cleared of serious fraud charges in a separate criminal fraud trial over the Autonomy case in the United States.
However, HPE is now seeking damages of £3bn, with the judge set to rule on the final sum soon.
A spokesman for HPE said: “In 2022, an English High Court judge ruled that HPE had substantially succeeded in its civil fraud claims against Dr Lynch and Mr Hussain.
“A damages hearing was held in February 2024 and the judge’s decision regarding damages due to HPE will arrive in due course.
“It is HPE’s intention to follow the proceedings through to their conclusion.”
However a UK judge has already ruled that the total sum of damages would be “substantially less” than HPE had sought.
Dr Lynch’s death means his widow, Angela Bacares, could now be liable for the damages claim in London.
Business Dr Lynch, who lived near Wickham Market, was among six people who went missing after a yacht they were travelling on capsized during a freak storm in August.
Specialist divers recovered seven bodies from the sunken superyacht, including Dr Lynch and his 18-year-old daughter, Hannah.
Dr Lynch and his daughter, Morgan Stanley International bank chairman Jonathan Bloomer, his wife, Judy Bloomer, Clifford Chance lawyer Chris Morvillo, and his wife, Neda Morvillo were lost when the Bayesian sank off the coast of Sicily.
The boat trip was a celebration of Mr Lynch’s acquittal in the fraud case.