Washington businessman Kingdon Gould Jr. has won a $1 million out-of-court settlement in a lawsuit accusing Sears Bank & Trust Co. of Chicago of reneging on a promise to help Gould rescue a struggling Illinois company.

The settlement was so large that Sears Bank yesterday was forced to restate its financial reports for 1981 to reflect the settlement with Gould. The bank itself is in trouble and lost a total of $7.4 million for the year, including the $1 million it agreed to pay Gould.

Gould's attorney, Martin Thaler, confirmed that the Washington businessman has agreed to the million dollar settlement after a three-year legal fight with Sears Bank, which is not affiliated with Sears, Roebuck & Co.

A former ambassador to Luxembourg and heir to the Gould railroad fortune, Gould is a prominent Washington businessman, an owner of Parking Management Inc. and a partner in the Mayflower Hotel.

Four years ago, Gould became involved in an attempt to resurrect Astron Manufacturing Co., an Illinois battery maker in which a frequent business associate, John W. Lyon, was an investor.

Astron was in what Gould's lawsuit calls "significant financial difficulties" at the time and Lyon had personally guaranteed a $2.5 million loan to the battery company from Sears Bank. After creditors forced Astron into involuntary bankruptcy and closed its doors, Gould began working on a plan to rescue the firm, according to documents filed in the federal court case in Chicago. The plan was thwarted when the bank refused to go through with loan financing.