In what could be the second shot of a bidding war for Equitable General Corp. of McLean, Liberty National Life Insurance Co. of Birmingham, Ala., yesterday offered $45 a share in cash for all of Equitable General's stock.

Last Friday, Great Southern Corp. of Wilmington, Del., offered $40 a share in cash or stock for the local insurance company, and Equitable General said the two companies had agreed in principle to merge.

Equitable General has about 2.9 million shares outstanding, making the Liberty National offer worth about $130 million.

Sources familiar with the company said they would not be surprised to see a counter offer from Great Southern or another bid for the company. In January Equitable General blocked a potential takeover by another firm by buying back a large blocks of its stock for $32.50 a share.

Equitable General officers did not comment directly on the new bid, which they said was received unexpectedly yesterday morning.

Officers of the company noted, however, that Liberty National's $45 cash offer would be fully taxable, making it less attractive to some shareholdersthan a tax free stock exchange offered by Great Southern.

Many Equitable General shareholders, including company exectives and owners of several large blocks, reportedly bought the stock for $1 a share or less. A cash offer of $45 a share would give these owners only about $25 a share after taxes.

Great Southern offered to buy up to 12 million shares of Equitable General for cash and to acquire all the shares in exchange for a new Great Southern convertible preferred stock paying a $3-a-year dividend.

Great Southern officials said yesterday they had not had time to study the Liberty National offer and could not respond to it.

Liberty National Executives in Birmingham could not be reached for comment.

The rival bids for Equitable General could come to a head next week. The company's annual meeting is Tuesday at 2 p.m. at the Ramada Inn in Falls Church.

Over-the-counter trading in Equitable General shares was suspended about 1 p.m. after the company said some announcement was coming. The stock, which traded at $29.50 bid, $30.50 asked a week ago, was quoted at $37.50 bid and $39 asked when trading was halted, up from $36 bid, $37.50 asked, on Thursday.

Equitable General Chairman Charles Phillips reportedly had rejected earlier merger or acquisition offers and had come under intense criticism from some stockholders.

Phillips, who is 75, has run the company for more than 40 years, and controls about 15 percent of its stock.

He and the company's management were sued in Fairfax County recently by three shareholders, who accused the company's executives of "gross mismanagement poor business judgement, breach of fiduciary responsibility and conflict of interest."

The lawsuit contends the management acted illegally and improperly in acquiring for the company large blocks of stock that had been held by Control Data Corp. of Baltimore.

Control Data sold the shares for $26.25 to American General Insurance Co., a Texas firm that indicated it might seek contol of Equitable General Saying the action was necessary to stop an unfriendly takeover, Equitable General in January purchased the stock for $32.50 a share.

The dissident stockholders contended that was too high a price and demanded Phillips and the board of directors repay nearly $2.9 million they claimed wsa misused in buying the shares.