Boston Public Library officials and supporters of keeping the Lower Mills branch open this week attempted to brainstorm ways to help money flow into the cash-strapped library system.

Library officials say the state is expected to face a “significant” budget gap in fiscal year 2012, which starts in July, and deep cuts in aid to cities and towns are likely.

Earlier this year, the Boston Public Library’s board of trustees voted to shutter four branches, including the one in Lower Mills, after arguing that the 26-library system needed to be modernized and cut back because of fiscal reasons. After intense outcry from state lawmakers and neighborhood residents opposed to the closures, library officials said they would keep the libraries open if money is found.

One local resident, Susan Lombardi-Verticelli, expressed frustration with the city’s pace in attempting to extract more in payments in lieu of taxes (PILOT) from local universities and hospitals. Fifty-three percent Boston’s 48.6 square miles is non-taxable in part because nonprofits like universities and hospitals are exempt from the property tax, city officials say. The property universities and hospitals own equals about $350 million in property taxes, while the city receives $15.7 million in PILOTs.

“The city has known about this issue for way too long,” said Lombardi-Verticelli, one of several dozen advocates who attended a Monday night meeting at the Lower Mills branch with library officials. “And yet we come here time and time again, cutting from public services.”

The city has PILOT agreements with 16 educational institutions and 12 hospitals, with the largest PILOT payments coming from Boston University, Massachusetts General Hospital, Harvard University, Brigham and Woman’s Hospital and Tufts Medical Center, according to a report released this week by the Lincoln Institute of Land Policy.

The city receives $4.9 million a year from Boston University, roughly 8.5 percent of what the university would owe if it paid normal taxes on its property, according to the report. The city collects $14.8 million a year in PILOTs from education and medical institutions who own property worth over $12.7 billion.

Another library advocate, David Vieira, president of the city-wide Friends of the Boston Public Library, noted that he frequently receives a promotional email from the New York public library’s gift shop touting reproductions of some of the artifacts in their collection. He said tourists would likely be interested in similar reproductions from the Boston Public Library’s collection.

“They’d love to take something back from the Boston Public Library,” he said. “There’s a cash cow hidden in those rooms upstairs. You need to milk that cow.”

City Councillor Maureen Feeney praised the idea. “You go to Museum of Fine Arts and you can purchase all sorts of printing,” she said. “These are the kind of ideas we need to look at long term.”

She also asked for advocates to stay involved in the budget process. “I promise you that as we move forward that this is going to be part of the dialogue as we approach next year’s budget, which will start in January,” she said. “What you’re giving us is the tools to find the solution.”

Library advocates also pitched the idea of allowing the library’s board of trustees to fundraise. They are currently prohibited by law from doing so.

The City Council passed a measure earlier this year giving them clearance to do so, but Mayor Thomas Menino has held off on signing the legislation, arguing that the board should set policy and the library’s foundation should raise money.

Material from State House News Service was used in this report.