Capitol Hill Hospital and four physicians have agreed to pay $400,000 in an out-of-court settlement to the family of a 22-year-old Southeast Washington man who died at the hospital 2 1/2 years ago.

The family of Charles E. Lucas claimed in a suit filed in D.C. Superior Court that he bled to death because the hospital failed to treat him promptly for a gunshot wound.

According to lawyers in the case, the hospital agreed to pay the family $160,000 in damages, while the physicians agreed to split the remaining portion of the settlement.

Nicholas McConnell, an attorney who represented the hospital and the physicians during the final settlement negotiations, said: "We're all tremendously relieved that we were able to settle. . . It was unfortunate that Mr. Lucas died. Assuming that everything possible had been done, perhaps he would have lived."

Lucas, a time-keeper for Donahoe Construction Co., was shot once in the buttock as he was being robbed outside a pizza parlor at 1401 25th St. SE on Nov. 5, 1980. Lucas was taken to Capitol Hill Hospital by city fire department paramedics. He died of internal hemorrhaging about two hours later, soon after physicians had begun surgery on his wounds.

In the suit, Warren Kaplan, the attorney for the Lucas family, alleged that Lucas' death was caused by the delay in getting the injured man into the operating room.

Surgeons operate at Capitol Hill on an on-call basis. Kaplan alleged that the hospital negligently failed to maintain a system under which surgeons would respond quickly enough to injuries such as Lucas'. Kaplan also maintained that hospital officials negligently failed to instruct emergency room staff to send cases to another hospital when a slow response might threaten a patient's life, and that the individual surgeons had failed to repond quickly to calls for help.

In papers filed with the court, the hospital countered that its system was adequate to handle emergency surgery cases and that it could not be held responsible for Lucas' death. The hospital also maintained that it had been forced to accept Lucas as a patient because city paramedics had ignored information that Capitol Hill's emergency room at the time was closed and that cases were to be transported elsewhere.

An attorney for the hospital, Richard Boone, said yesterday that the hospital was evaluating its on-call procedures at the time of the incident and continued to do so until recently. He said the hospital has since recruited additional doctors to practice at the hospital on call.