It is believed to be one of the largest - if not the largest - challenge grants ever offered by an individual in the region.
Lenfest thinks the cause is that important.
"We have the opportunity to build the first national museum dedicated to the American Revolution in the historic district of Philadelphia," Lenfest said in a Monday interview. "I think that's the missing link in the chain of events that led to independence. So, I think it's important to have it."
The $40 million challenge, if met, would provide the museum with $80 million. In addition, the state has authorized up to $30 million in capital redevelopment funds.
The cumulative total would be enough to launch construction, said Michael Quinn, the museum's chief executive and president.
"My sense is that the board would move forward with that," Quinn said.
The museum is putting together a capital campaign that would include $115 million for building construction and exhibition planning and implementation, and $35 million for endowment, Quinn said.
The building would probably come in for less than $100 million, although officials could not come up with hard construction numbers at this stage of the planning process.
Lenfest also said the museum was working out a "very conservative" business plan for operations, based on projected visitorship, but he had no precise numbers. Quinn said officials are "still scrubbing" the numbers and are not prepared to discuss planning publicly at this point.
"We're just not certain enough to put it out there," he said. "Different models are resulting in different numbers."
Nor will any kickstarting contributions be announced yet to meet the Lenfest challenge, Quinn added.
"We're working on that and we are hoping to make that announcement very soon," he said.
Lenfest has been a strong supporter of the museum since its beginnings and he has not been hesitant with his financial backing. He acquired 78 acres of Valley Forge land for construction in 2007 for $4.1 million. He also also contributed another $5 million for the project, according to previously published reports.
But plans for the museum - which would house the contents of the former Valley Forge Historical Society - faced shifting opposition from Montgomery County residents, the National Park Service and local officials over land use, size and other matters.
In 2010, the revolution center, the private nonprofit that operates the museum and is chaired by Lenfest, worked out a deal with the park service, swapping its Valley Forge property for the site at Third and Chestnut Streets where the old Independence National Historical Park Visitor Center was built in 1976.
Independence Park's popular archaeology lab was compelled to leave that space, and is now located in a small building on Walnut Street.
The park service will retain part of the old visitor center, where parkwide cooling machinery is housed. The rest of the building will come down when the revolution center begins construction.
When might that be?
"We've done enough planning to conclude that if everything moved as fast as it could . . . if it were fast tracked, it's conceivable to open this museum by the end of 2015," said Quinn. "That would be the fastest."
In the meantime, Lenfest remains as strong in his support as ever. He believes the challenge grant approach can be an effective tool.
For one thing, Lenfest has funded challenge grants at Washington and Lee University, his alma mater, and at Columbia University, where he attended law school. He has gone the same route at the Philadelphia Museum of Art.
"They turned out very well," he said. "So its a familiar thing to me."
Those challenges, however, were aimed at endowing academic chairs and curatorial positions, which require much less money. Building a $100 million museum with a $40 million challenge is quite a different matter.
"It's a major opportunity," Lenfest said. "It's the missing link in the whole series of events that made this country."
And although he announced several years ago that he had given virtually all his money away, the museum challenge has been a long-planned project.
"We've given away the bulk of our wealth already," he said. "This $40 million was planned long ago."
Contact culture writer Stephan Salisbury at 215-854-5594, email@example.com, or @SPSalisbury on Twitter