Sears, Roebuck and Co., the nation's largest general merchandise retailer, yesterday reported its best third-quarter profits ever and Woodward and Lothrop, Washington's biggest independent department store firm, said its third quarter earnings also improved, although not as much.

Sears' net income for the period ended Oct. 31 rose to $225 million (71 cents a share), up 41 per cent from the $259 million (50 cents) of a year ago. Sales climbed 19 per cent to $4.5 billion.

For the first nine months of the year, Sears, earned $586 million ($1.84) on sales of $12.2 billion, 54 per cent above the prior year's earnings of $381 million ($1.20) on sales of $10.5 billion.

Woodies net earnings for the quarter increased to $2.8 million, $1.18 a share) up 5.2 per cent from last year's $2.7 million ($1.12). Sales increased 3.2 per cent to $60.4 million from $58.6 million.

In both sales and earnings, Woodward and Lothrop's third quarter helped compensate for sluggish performance earlier in the year. After the first nine months of the year, the chain's sales are running 2.8 per cent ahead of least year - $169 million versus $164 million - but profits are fractionally behind, $5,897,000 compared to $5,911,000.

Woodies' president Edwin K. Hoffman said tight expense control and improved profit margins allowed the company to increase earnings faster than sales, which he said were hurt by unseasonably warm, wet weather.

Radiation Systems Inc. a Mclean maker of antennas, reported earnings of $140.000 (18 cents a share) on sales of $1 million for the quarter ended Sept.30. Earnings for the corresponding period a year ago, if fully taxed, would have amounted to $ 76,000 (10 cents) on similar sales, said president Harry Letaw, Jr., who was recently reelected after the company's annual meeting.