What was going on when I was born?

New orders for machine tools continued to slide in March, and industry analysts now say that orders this year will slip below the depressed levels of last year. Orders for March dropped 61.2 percent, to $135.3 million, from $349 million in March 1981, and fell 17.4 percent from February's level of $163.8 million. So far this year, orders are down by 45 percent, according to the National Machine Tool Builders Association.

Despite his avowal that Bob Lemon would manage the Yankees for the entire 1982 season, no matter what the team's record, George Steinbrenner dismissed Lemon yesterday for the second time in three years. Gene Michael, whom Steinbrenner dismissed as manager last September, will replace Lemon only 14 games into the season. The change, announced at Yankee Stadium at 8 o'clock last night, is the eighth in the 10 seasons that Steinbrenner has been the principal owner of the Yankees. Six of the changes have occurred in the last four years, and three of the managers involved -Michael, Lemon and Billy Martin -have held the job twice. The Yankee players were gone, following their a 3-1 victory over Detroit, by the time the move was disclosed. However, the players generally and Rich Gossage specifically have blamed Steinbrenner for the team's problems.

With conditions improving at New York City's public shelters for the homeless, officials say the shelters have begun attracting hundreds of people who might otherwise remain in other housing. These people represent a significant change, city officials say, in the kind of homeless person using the shelters, which usually house people who have been living on the streets. Instead of continuing to live with friends and relatives who do not want them, many young, able-bodied men and women, particularly those who have just lost jobs, are seeking public shelter. City officials say this new group helps account for the fact that, as the weather has become warmer, there has been no decline in the number of people in the shelters.

IT was cruel and it was ugly: all the talk about Bob Lemon being given a full year to manage the Yankees, a last hurrah with dignity and patience. ''There will be no change this year,'' Steinbrenner said last Dec. 9. ''I wouldn't care how the team is doing. I'm not going to make a change in 1982 unless it's dictated by something other than how the team is doing.'' Lemon knew what garbage this was. With his drinker's wisdom, he would grimace every time Steinbrenner's promise was discussed. ''I'm just keeping the seat warm,'' was Lemon's blunt assessment. He didn't win, and he is gone - gone so fast, so dismally, that Yankee Stadium may become even grimmer, even more funereal, than usual.

A review last Tuesday of the City Opera production of ''Medea'' incorrectly reported Eileen Farrell's performance history in the title role. She sang the role in San Francisco in September 1958.

The depressed economy slashed corporate profits in the first quarter. Hardest hit were the auto, steel, airline and other cyclical industries. Although banks profited handsomely from high interest rates, brokerage houses heavily dependent on retail trade showed large declines. (Page D1.)

Future American mediation efforts in the Falklands crisis were thrown into doubt tonight when Argentina's Foreign Minister asked for a postponement of a meeting with Secretary of State Alexander M. Haig Jr. and later said Argentina had suspended talks because of Britain's military action in South Georgia. Foreign Minister Nicanor Costa Mendez said he had decided not to see Mr. Haig as planned because the attack by the British led Argentina to believe that ''the negotiations with Britain had terminated.'' The State Department, however, declined to say the American effort had ended. It said, shortly before Mr. Costa Mendez spoke, that Mr. Haig had had long telephone conversations this afternoon with the Argentine Foreign Minister and would speak with him Monday.

Last Friday evening, top executives of the Wickes Companies, one of the nation's largest retailers, gathered at the plush Century Plaza Hotel in West Los Angeles to discuss the company's shaky finances. By the time dinner was over, it was clear to Sanford C. Sigoloff, Wickes's new chairman, that the company was rapidly failing and that bankruptcy was the best solution. Difficult though the company's problems were, Wickes's biggest problems may lie ahead. In particular, the company faces the task of convincing its suppliers, who have already shied away from filling orders, to resume shipments to stores already depleted of stock.

Yesterday, when the long-lost sun had warmed the sidewalks on West 86th Street, Marian Ekberg stepped out from her room with her cane for the 80th spring of her life. She caught her breath at the sight of the concourse of people, with strollers and picnic baskets in hand, headed toward Central Park. ''What a perfect day!'' she said, echoing the feeling of millions. ''It couldn't be nicer.'' On a path in the park, a tall graying man walked with a girl perhaps 12. Her unneeded sweatshirt was draped around her shoulders, and the man was holding on to a sleeve. ''It's hard enough to have a relationship with a friend, let alone a marriage,'' the man was saying.

LOUISVILLE, Ky. WHAT began on winter and spring nights of 1979, when 34,497 thoroughbred mares delivered foals who might have run in this year's Kentucky Derby, is reaching its conclusion this week amid only one certainty: the best of that generation will not be running for the roses. The 108th Derby on Saturday will be a race among survivors, tinged with anticlimax and lacking a solid favorite. For the first time in at least a decade, none of the four top-rated 2-year-olds of the previous year has made it to Louisville. Deputy Minister, the juvenile champion, injured an ankle in February. Timely Writer, who developed into the heavy pre-Derby favorite, narrowly survived emergency abdominal surgery last week and is recuperating. Stalwart, the best California-based prospect in years, has been retired with damaged tendons. D'Accord simply has forgotten how to win and is being examined for possible defects. The roster of wounded also includes Conquistador Cielo, Distinctive Pro, Aloma's Ruler, Victorian Line, Hollywood Henderson and Tropic Ruler. Lets Dont Fight was beyond repair and was humanely destroyed. Even some of those who had risen to take their places, such as Linkage and Shimatoree, are now too short-winded or weary to run.

The slumping United States economy severely depressed the earnings of a broad variety of American companies during the first quarter, according to reports issued thus far. In some industries, performances of companies differed widely, but the airline and steel industries and other cyclical sectors were particularly affected. Companies in other, relatively less cyclical industries fared better. Several banks showed substantial increases in earnings, but on Wall Street, the large retail brokerage houses had a rough quarter.

In a hotel ballroom in New York the other day, a thousand people listened in engrossed silence as Senator Daniel Patrick Moynihan delivered a nine-page treatise on the merits of American government and the principles of the founding fathers. Along the way, the Senator found reason to touch on nuclear war, the Middle East, the Atlantic alliance and Argentina. Some five years earlier, at the start of his Senatorial career, Mr. Moynihan expounded week in and week out in Senate Banking Committee hearings on the need to rescue a nearly bankrupt New York City. His persistence was a crucial factor in persuading reluctant legislators to pass Federal loan guarantees for the city. During his first term as a Democratic Senator from New York, Mr. Moynihan, who announced his candidacy for a second term Saturday, has strived to fulfill two roles. One is that of a diligent legislator who faithfully represents his constituency, and the other is that of a leader in the realm of national issues and ideas. On Capitol Hill, where Senators are often described as belonging to the ''old school'' of, for example, Daniel Webster, versus the ''new school'' of a bureaucratic legislator, the 55-year-old Mr. Moynihan is viewed as being of the ''old school.''