Lucky Stores Inc., target of a takeover attempt by Salt Lake City-based American Stores, had record first quarter earnings from continuing operations totaling $31.4 million, or 81 cents per share, on sales of $1.63 billion.

The first quarter results included expenses of $4.4 million after tax, or 11 cents per share, that resulted from tender offers by American Stores and Gibbons, Green, van Amerongen, a New York investment firm. Lucky had agreed to a $61 per share merger with Gibbons, Green, but American Stores this week said it would raise its $45 offer, made in March, to $65. Lucky said it is evaluating the new, $2.5 billion offer from American.In the prior year, Lucky's earnings from continuing operations were $30.2 million, or 79 cents per share, on sales of $1.75 billion. The 1987 first quarter results included after tax earnings from Eagle Food Stores totaling $2.5 million, or 7 cents per share, on sales of $245.7 million. Eagle was transferred to a newly formed limited partnership in November 1987.

"Before the expenses of the tender offer, our continuing operations earned 92 cents per share compared to 72 cents per share last year without Eagle," said John M. Lillie, chairman.

"The higher earnings were attributable to the continuation of strong sales momentum in our northern and southern California operations, close attention to expense control and a decline in the effective tax rate.

"Gross margins were intentionally reduced from year ago levels in our California, Nevada and Arizona operations in response to competitive market conditions and to reaffirm to consumers our low price leadership position.

"This resulted in lower gross margins overall but produced an outstanding 8.7 percent sales increase in our California stores."

Lucky operates 486 stores under the Lucky, Food Basket, Advantage and Kash n' Karry names in California, Nevada, Arizona and Florida. During the first quarter, five new stores were opened including the first Advantage Store, located in San Diego.