Regardless of income, Mr. Adams said, “we know anecdotally and through research that finding a place that’s going to be welcoming to you as an L.G.B.T. person is quite a challenge.” The research includes a 2014 study by the Equal Rights Center, a Washington nonprofit, that found that 48 percent of older lesbian, gay, bisexual and transgender couples looking for housing experienced adverse treatment. The anecdotes are populated by bullies. “Often these stories we hear are about peers,” Mr. Adams said. “They’ll mistreat, ostracize and marginalize their L.G.B.T. neighbors.”

Such problems for older people are, sadly, not surprising, he said, because “if you look at research, you find that the older a person is, the more likely he is to harbor bias.”

The two new Sage buildings — the 145-unit Ingersoll Senior Residences in Fort Greene, Brooklyn, and the 82-unit Crotona Senior Residences in the Bronx — were financed under Mayor Bill de Blasio’s 10-year housing plan aimed at creating and preserving 200,000 units of affordable housing. Both are expected to open in summer 2019 and to have long waiting lists.

More than 1,000 people have already expressed interest in becoming among the first to move in, Mr. Adams said. A lottery to determine the first batch of residents will open in January 2019.

“We know for sure that the demand for these apartments is going to outstrip the supply,” he said, which seems to be a common problem across the United States.

When the John C. Anderson Apartments, an affordable six-story building with 56 units in Philadelphia, opened in 2014, the waiting list was capped at 100, said Ed Miller, an on-site social worker. The building, named for a local City Council member who died in 1983, features framed photos of the 1969 riots at the Stonewall Inn in New York in the hallways and a mural in a common space depicting the history of Philadelphia’s lesbian, gay, bisexual and transgender movement.