The Limited Inc., the aggressive fast-growing chain of women's clothing stores, yesterday announced it had reached an agreement in principle to buy the Lerner Stores division of Rapid-American Corp. for $260 million.

The announcement from the Ohio-based chain capped weeks of speculation that it was about to buy the 800 Lerner stores, which sell budget-priced women's apparel.

The Limited, which also owns Victoria's Secret, Lane Bryant, the Limited Express and Sizes Unlimited, said it hopes the acquisition will be completed within 30 days. "We're adding another niche in the women's market" that The Limited serves, said Al Dietzel, Limited's vice president of finance. The acquisition "is consistent with our basic strategy to be a specialty shop for women."

Limited, with a total of 1,450 stores nationwide, had sales near $1.4 billion for 1984. Lerner's annual revenue was estimated at about $700 million for the most recent fiscal year.

With Limited's plan to grow to more than 2,000 stores by the end of 1985 and with the addition of Lerner's, some analysts predict Limited's revenue will top $2.5 billion at year's end.