Mayor Rahm Emanuel and his emissaries are trying to persuade a fractured Friends of the Parks board to drop its lawsuit blocking construction of the Lucas Museum near Soldier Field by dangling support for an even bigger lakefront dream: the “Last Four Miles” of lakefront parkland.

In 2009, Friends of the Parks marked the 100th anniversary of Daniel Burnham’s Plan for Chicago by unveiling a visionary sequel that would add 525 acres of lakefront parkland and extend public access to Lake Michigan from the Evanston border all the way south to the Indiana border.

It was called the “The Last Four Miles Plan” because that’s how much new lakefront parkland it would take to fill in the gaps — from 71st to 95th streets on the south and from Hollywood to Howard Street on the north.

Devised by architects, urban planners and engineers after years of community workshops, the plan had a $450 million price tag, but no apparent source of funding.

The cost of using lakefill, sand, stone and concrete sea walls to create a continuous chain of parks, beaches, lagoons and bike trails along the 30-mile Lake Michigan shoreline has climbed even higher since then.

So has the cost of negotiating access to the private land controlled by a handful of condominiums on the north lakefront.

Now, top mayoral aides and intermediaries are dangling Emanuel’s formidable support for a plan that could easily take 20 years to complete for City Hall’s more immediate concern: keeping movie mogul George Lucas’ interactive museum in Chicago.

Emanuel already has raised property taxes by $588 million for police and fire pensions and school construction. He has offered to raise property taxes by an additional, $175 million for teacher pensions. He also needs a new funding source to save the Municipal Employees Pension fund, the city’s largest.

With all of those financial pressures closing in on Chicago, it’s not clear how much money Emanuel could devote to the noble goal of creating more lakefront parkland or where that money would come from.

But even if the mayor offers to make a small down payment and use his still formidable clout to win federal funding for the ambitious project, it just might be enough to convince Friends of the Parks that it should lift the legal blockade.

Friends of the Parks Executive Director Juanita Irizarry did not return repeated phone calls. Board Chairman Lauren Moltz could not be reached.

Board member Fred Bates said a Friends of the Parks board that was admittedly deeply divided over the Lucas Museum issue was “always open to dialogue.”

Bates said the goal of completing the last four miles of Chicago’s lakefront is a “wonderful thing,” adding, “I’m sure it will happen someday.”

But he argued: “It’s a separate issue,” and added, “I don’t think anybody is offering anything.”

Board member Oscar D’Angelo said he’s been “out of the loop for a while” and therefore unaware of the recent negotiations.

But he said: “I don’t think the Lucas Museum belongs in Chicago. It belongs in California. That’s where his work was done. I don’t think Chicago had anything to do with his success. I’m strained to find the rationale.”

Mayoral spokeswoman Shannon Breymaier issued a carefully worded statements that alluded to intermediaries but made no mention of the “Last Four Miles Plan.”

“A number of groups in the city have expressed a high degree of interest in making sure Chicago does not lose the Lucas Museum and its tremendous economic, educational and cultural benefits Those groups have gotten involved to try to find a way to ensure the museum and the opportunities it would create stay in Chicago,” Breymaier wrote.

Emanuel’s behind-the-scenes offer to get behind the “Last Four Miles Plan” is the latest in a series of desperation moves to keep the Lucas museum in Chicago.

Last month, Emanuel asked the federal appeals court for a “writ of mandamus” that, if granted, would essentially order U.S. District Judge John Darrah to dismiss a Friends of the Parks lawsuit that Darrah kept alive challenging the mayor’s original plan to give Lucas 17 acres of lakefront land near Soldier Field.

Darrah has already rejected the city’s motion to dismiss and sympathized with Friends of the Park’s central argument: that a 99-year lease “effectively surrenders control” of prime lakefront property to a museum that is “not for the benefit of the public,” but would “promote private and/or commercial interests.”

Friends of the Parks responded with a vow to carry on the fight in state court if the federal appeals court rules in Emanuel’s favor.

Before that legal maneuver, Emanuel offered to demolish McCormick Place East to make way for the Lucas Museum, only to have Friends of the Parks declare its intention to challenge that site, as well.

That prompted Lucas’ wife, Chicago businesswoman Mellody Hobson, to say that she and her husband were “now seriously pursuing locations outside of Chicago” after a two-year process that she claimed had been “co-opted and hijacked” from the outset by “a small special interest group.”

Now Emanuel is throwing yet another Hail Mary pass. He can only hope that a Friends of the Parks board that has been under intense pressure to change its mind will finally see the long-term benefit of a larger trade-off.