The call by the All Party Parliamentary Group (APPG) on Fair Business Banking comes after the publication online on Tuesday of an internal 2013 report alleging serious misconduct by the lender over the handling and disclosure of the fraud.
The lawmakers said allegations that HBOS had concealed the fraud, one of Britain's worst-ever banking scandals that saw six people jailed for a total of 47 years last year, should be subject to "full, forensic and expeditious investigations by regulators".
A Lloyds spokeswoman reiterated the bank's statement on Tuesday that the internal 2013 report had been provided to Britain's Financial Conduct Authority (FCA) and to the police in 2014.
KPMG did not immediately respond to requests for comment outside regular UK business hours.
The internal report published on Tuesday by Scottish businessman Neil Mitchell, a frequent critic of Britain's big banks, alleged that HBOS executives knew of the fraud as early as 2004 and failed to properly disclose it, with far-reaching implications given Lloyds' takeover of HBOS in 2009.
In its statement on Tuesday, Lloyds did not address the substance of the report's allegations that it misled investors over its financial health by not disclosing the fraud earlier.
Britain's financial watchdog is conducting a probe into HBOS and what its executives knew of the fraud, while a retired judge is probing whether Lloyds then properly investigated the incident after it brought HBOS in 2009.
The report, written in 2013 by a former manager at the bank after she had taken her concerns to the police, stated that Lloyds mishandled its investigation and disclosure of the fraud after it took over HBOS in 2009.
Lloyds said on Tuesday that the former manager began looking into the bank's handling of the fraud case on her own initiative, and was then asked to write the report when she alerted the bank's audit department.
The report said that if HBOS had properly disclosed the fraud in its 2007 annual report, the 4 billion pound 2008 rights issue that stabilized its financial position and its subsequent takeover by Lloyds would not have happened.
Lawmakers last week urged Lloyds to publish the report, which the bank had declined to do on the grounds it contained sensitive information about its customers. Neil Mitchell said publishing it was in the public interest.
The APPG also published the report on Thursday. It said it would press for a new investigation into KPMG's audit of HBOS in 2008, which it said "gave the bank a clean bill of health only two months before it hit financial difficulty."
(Reporting by Emma Rumney in London; Additional reporting by Ismail Shakil in Bengaluru; Editing by Nick Tattersall and Toni Reinhold)