Lockheed Corp., citing increased sales and lower interest costs, yesterday reported substantially improved earnings for both the third quarter and the first nine months of the year.

The aerospace company, based in Burbank, Calif., said third-quarter earnings were $55.1 million ($2.82 a share), up from $38.8 million ($2.28) a year ago. Third-quarter sales were up $59 million. Nine-month earnings were $144.4 million ($7.73) on sales of $3.9 billion, up from $103.2 billion ($6.22) on sales of $3.6 billion.

Lockheed said the earnings and sales figures reflect continuing operations; 1981 data was restated to exclude the company's L1011 Tri-Star program, which is being discontinued.

Dallas-based American Airlines Inc. reported third-quarter earnings of $17.8 million (45 cents), up from $14.4 million (39 cents) in the year-earlier period. For the first nine months of the year, American had a loss of $23.3 million ($1.07), compared with net earnings of $67.7 million ($2) in the 1981 period.

American Chairman Albert V. Casey, chairman of the Dallas-based airline, said that both passenger traffic and yield -- the average amount of revenue received per passenger per mile -- were disappointing during the third quarter. Traffic was up just 4 percent in the quarter because of the sluggish economy, he said, and discount fares kept yield down.

From now on, the company noted, it will be reporting as AMR Corp. The change was made Oct. 1.

Polaroid Corp. net earnings for the third quarter climbed 30 percent to $8.3 million (26 cents), compared with $6.4 million (19 cents) in last year, the firm reported yesterday. But sales dropped 12 percent to $316.8 million from $359 million in the 1981 third quarter.

In the first nine months of the year, net earnings were $13.9 million (43 cents), compared with $29.4 million (89 cents) a year ago. Sales were $901.2 million compared with $974.3 million.