Museum bosses have one last chance to secure approval for the project and quash rumours that the earmarked funding has become another victim of the cash drain from the arts in the run up to the London 2012 Olympic Games.
The decision is the latest twist in the ongoing saga surrounding the proposals to build a Modernist glass and ceramic extension on the rear of the Grade I-listed museum.
It was feared that £4.9 million promised by the HLF towards the contentious scheme in the heart of Bath would be pulled after the local council unexpectedly rejected the project in July ( Eric Parry's rejection in Bath could mean curtains for Holburne Museum ).
It is understood the museum will close if Parry's proposed £10 million, 800m2 addition fails to win its appeal against the council's decision.
Alexander Sturgis, the museum's director, said: 'I can't tell you what a relief the Lottery's decision is. We have had two very anxious months since the council's devastating decision. Our greatest fear was that we had lost the grant and with it any chance of a future towards which we have all been working for many years.
The decision allows us to continue to try and find ways to deliver our plans, which will see a museum of real quality able to punch its weight and attract and engage a much wider audience through exhibitions and education. Although we are confident we would win our appeal against the council's decision we have also been having constructive talks with the council, the planners, and our architects in an attempt to reach a swifter resolution. With continuing support, I am hopeful we will get there.'
The museum itself has already raised £4 million towards the project at the top of Great Pulteney Street.