Among the examples cited from the agency’s own 2014 records is a patient with lupus who had undergone a lower-limb amputation and used a wheelchair. The patient’s doctor had ordered 27 rehabilitation visits and 38 nursing visits to be made over a 60-day period. The agency provided none of the rehabilitation visits and only five nursing visits during the two-month period, but it collected a full $3,537 in government reimbursement, the lawsuit says.

Similar cases cited in the complaint involve patients coping with the aftereffects of a mastectomy, a kidney transplant, a hip fracture and a knee replacement, some with complications from diabetes, high blood pressure or heart disease, others with bedsores and Alzheimer’s disease. All are said to have received a fifth or less of the care prescribed, without the agency notifying them, their doctor or the government of the reduction in services.

Mr. Lacey tried to get executives at the agency to correct the fraud and misconduct, to no avail, according to the lawsuit. Through his lawyers at Constantine Cannon, he declined to talk about the case. Under the rules of this type of suit, he could be awarded up to 30 percent of any money the government recovers.

The lawsuit depicts an agency in escalating turmoil. Regional managers warned of agency patients languishing without care, but agency policy, enforced by the chief executive, was still to accept all patient referrals in order to maximize billings, the suit says, despite a shortage of staff to provide the ordered services.

“The scope of V.N.S.N.Y.’s failure to provide its patients with the level of care they require has been increasing and engendering a growing chorus of complaints,” the lawsuit says, quoting heated exchanges at executive meetings from April to July 2014.

At a meeting that Mr. Lacey attended with several other agency vice presidents that April, for example, the manager overseeing home health care services in Brooklyn warned that in her region alone, there were 600 patients for whom the agency was unable to provide the ordered therapy services, and that even if the services could eventually be provided, it would be too late for the patients to derive any benefit.

Similar concerns were voiced by those overseeing the agency in Manhattan, Queens, the Bronx and Westchester. An internal report showed that nearly half the 5,000 patients referred for rehabilitation services during that period had gone without the prescribed services; another internal report, titled “Therapy Services Not Provided as of May 9,” showed 2,038 patients still waiting, including some who had gone eight weeks without any care.