The estate of Lehman Brothers has sought to match Sam Zell's $1.33 billion bid for a 26.5 percent stake in Archstone, sharpening the rivalry for control of the multifamily housing giant.

Lehman mailed its offer to Bank of America and Barclays, which together hold a 53 percent stake in the company. Lehman currently controls the remaining 47 percent and is seeking to increase its ownership to 73.5 percent.

Lehman has also sued Bank of America and Barclays for a breach of contract in order to block transfer of Archstone's interests to Zell's Equity Residential, which it said would give Lehman time to make its own purchase.

A spokeswoman for Equity Residential told Bloomberg that Equity will wait until Lehman potentially closes on the 26.5 percent stake before acting further. Equity could buy the remaining 26.5 percent of the company that the banks control, but pricing hasn't been determined.

Lehman and real estate company Tishman Speyer bought Archstone for $22 billion in 2007 near the height of the market, with Bank of America and Barclays providing financing. Archstone was converted from a publicly traded company to a private one as part of the process.

After Lehman collapsed in 2008, it has been at odds with the banks over the future of Archstone. (Tishman Speyer has since exited the investment.) Lehman had favored bringing the company public again with an initial public offering or selling the entire company, while Bank of America and Barclays resisted an IPO and sought to sell their individual stakes.

Sam Zell, whose Equity Residential controls a substantial portfolio of its own residential buildings, became a lead candidate to buy Archstone in November, further complicating the ownership dynamic. Zell seeks the 26.5 percent interest in Archstone as a foothold for a complete takeover of the company, a move that Lehman is resisting because, in part, it believes Zell's valuation of Archstone is too low.

Archstone has over 70,000 apartment units in the United States and continues to make acquisitions, including a $131 million purchase of a Manhattan apartment building announced earlier this week. The strength of the rental housing market -- in contrast to the weak sales market -- has boosted the company's value in recent years.

Lehman will need court approval by Jan. 24 to make the bid.