When stockholders of Government Employees Insurance Co. are called to order this morning at 10 o'clocks, for their annual meeting at the Shoreham Americana Hotel, one man in the audience will find it difficult to fight off an attack of nostalgia.

Lorimer Arthur Davidson, a 75-year-old Quebec native who first became associated with the local auto insurance firm in 1948, will be attending his last meeting as a company director.

The Davidson years at Geico have covered mostly ups but a few downs over three-fourths of the company's entire existence. His early experience as an investment banker, combined with his attraction to the Geico concept of selling lower-cost insurance without agents, first provided by the capital base from which the company expanded.

As chief executive from 1958 to 1970, and as president or chairman during those years, Davidson formed affiliates in related business and phenomenon. Along the way he helped many small investors from the early years reap a fortune.

Finally, when Geico headed toward what looked to be certain disaster in 1976, Davidson's years of semi-retirement eneded and he was working virtually every day as one of a select committee of five directors named to seek new leadership.

Or, to quote Davidson, "to straighten things out."

"Dave" Davidson, as he is known to his associates, has had two favorite activities in recent months - his continued involvement at Geico as a member of the directors' investment committee and vigorous efforts to improve his game of golf.

"There are no clouds in the sky any more," but the period from December 1975 to mid-August 1976 "was quite a grim time, the worst of times, our beloved Geico was threatened with bankruptcy," he said in an interview.

Davidson went to sleep each night, "not to sleep but wondering whether I would wake and see destruction of a firm that 30 years ago had assets of $4 million compared with about $1 billion today.

Having helped find new management plus adequate capital to prevent insolvency and produce record profits last year, Davidson is convinced the companys greatest business growth is "yet to come."

The main factor, in his view, is that "the idea that made Geico a success . . . is just as valid today as [in 1936], high quality insurance at lower rates, with no agents."

Competition is tougher and Geico no longer will be able to undercut other firms, rates by as much as 25 percent, but good customer service and premiums that are priced "moderately less" than those offered by competitors promise growth, he said.

"The last two years were not the end of an idea, just a bad chapter in a broad record of progress," said Davidson, who now plans some travel and a three-month stay in Florida next year.

Davidson said his home will remain in Washington, however. And there's now way Geico can move someone else into his office: Davidson has an unusual lifetime contract with the company, requiring him to work 90 days each year as a consultant.

But don't look for Dave at Geico on balmy days. He can select the 90 days he wants to work and golf will win out when the sun shines.

THE LOCAL TICKER - One parting word of interest to investors was Davidson's revelation that Geico is about to re-enter the stock market, buying a "modest amount" of blue chips.

With the Dow Jones industrials above 770. Davidson said the danger of a further sharp decline now appears "minimal." The company is attracted to stocks of leading firms selling at 7-to-9 times earnings but yielding up to 7 percent annually in dividends. . . .

Other investors, meantime, obviously have found a new appeal in to the B. F. Saul Real Estate Investment Trust, the largest trust in the D.C. area. From an early low this year of $3.75 a share, Saul has been moving up steadily on the New York Stock Exchange to a high this week of $7. in active trading (243.000 shares in March, very unusual).

Market watchers attribute Saul's upturn to renewed interest generally in REITS, to a book value lower than the worth of properties owned and to expectations that dividends will resume in the next year. . . .

Ferris & Co., the Washington securities firm has forecast "above average" earnings and dividend growth for the next serveral years by Washington Gas Light Co., a long-depressed area "blue chip."

William Godden, Ferris research director, says WGL's ability to add new customers again and expanded natural gas supplies should help reduce the volatility of the firm's earnings record.

One problem for WGL: Virginia's Attorney General has challenged the utility's acquisition of Davenport Insulation, a manufacturer of controversial cellulose insulation.