Despite higher interest rates, more real estate was sold in the District over the summer than in either of the first two quarters of the year, pushing the nine-month volume very close to the total for all of 1983, according to data compiled by Rufus S. Lusk & Son Inc.

A total of 7,036 properties valued at $1.24 billion have changed hand so far this year, compared with 7,349 valued at $1.31 billion through all of last year, the report said.

And for the first time ever, mortgage credit in the city topped $1 billion in a quarter, though more than one-third of it went into the leveraged buyouts of Woodward & Lothrop and Dart Drug, Lusk found.

Lusk is a real estate information and publishing company that tracks property transfers in the area.

Its quarterly report for the District also disclosed:

* In a new record for a private residential sale, Mr. and Mrs. R. O. Gordon sold two adjacent properties at 3238 and 3240 R St. NW for just under $3 million.

The recorded buyers in the all-cash sales were nominees, but they were acting on behalf of Robert Bass of the wealthy Bass family of Fort Worth.

* Many of the most expensive properties involved the diplomatic community. The government of Singapore bought 4229 Lenore La. in the Forest Hill section from Mr. and Mrs. Thomas B. Wilner for $1.2 million, while the State Department bought two other properties in the same area -- 3500 Williamsburg La. NW for $850,000 and 3514 Williamsburg La. for $550,000.

It was not known whom the department was representing in those deals.

Also, the government of Santa Lucia, a Caribbean nation independent since 1979, bought 3100 Cleveland Ave. NW for $496,820, borrowing $400,000 of the purchase price from First Maryland Savings & Loan. Some 1,344 single-family dwellings were sold in the quarter, compared with 1,280 in the previous three months, and condominium sales totaled 664, up from 605 in the second quarter.

* Though unit volume was up, the average price of a single-family home was essentially flat -- $121,958 compared with $121,250 in the second quarter -- and the average condo price fell from $88,816 to $84,855.

* Seller financing continued to be the largest single source of mortgage loans. Sellers took back 376 first trusts, 20 percent of the 1,887 such loans in the quarter.

* Among institutional lenders, Perpetual American Federal Savings Bank was the leader with 119 first trusts totaling $13.4 million. First Washington Mortgage was second with 93 loans totaling $9.1 million, and Dominion Federal Savings & Loan was third with 66 for $4.9 million.

Goldome Realty Credit Corp., the leader for the previous 18 months, fell far back, with 18 loans for $2.5 million.

* Some 134 commercial properties changed hands, valued at a total of $128.7 million. The number of transactions was up from 127 in the second quarter, while the dollar volume declined from $177.6 million, but the second-quarter figures included a $50 million transfer by the Bank of Nova Scotia of 1300 New York Ave. NW to a U.S. subsidiary.

* Lusk notes that the tax assessments of many of the expensive properties are well below the purchase prices. The $3 million R Street properties sold by the Gordons were assessed at a total of just under $1.1 million.

The property that Singapore paid $1.2 million for had been assessed at $445,000. And a piece of commercial land at 15th and I Streets NW, bought by Prudential for $25 million from the United Mine Workers, was assessed at $10.4 million.