Royal Watch: Speculation is once again bouncing its way through the pages of the London tabloids that Randy Andy, sometimes known as Prince Andrew, is about to get married. It seems that his latest girlfriend, Sarah Ferguson, is in Switzerland on a skiing vacation with Prince Charles and Princess Diana, and the speculation is that Diana is giving the 26-year-old daughter of Charles' polo manager lessons in princess-ship.

Andrew's mother, the dour Queen Elizabeth, is said to approve this time. She has suffered through his other romances, such as the well-publicized one with American actress Koo Stark, sometime-star of soft-core-porn films. A sales executive with a printing firm, Ferguson is a lady of the required blue blood and is a direct descendant of Charles II. Ferguson is now available, since she recently broke up a four-year romance with a rally driver 22 years older than she. Her father, Maj. Ronnie Ferguson, is undoubtedly as pleased as the queen at this turn of events.

Andrew, a Royal Navy helicopter pilot, is on NATO exercises in the North Atlantic, and the queen's press secretary, Michael Shea, who was here with Charles and Diana for their visit, said of the stories of the pending marriage: "We are not going to comment on wild speculation." But then he usually says something like that. To Tell the Truth

Secretary of State George Shultz said he would resign rather than be among the thousands of employes the Reagan administration planned to require to take lie detector tests. The upcoming edition of Discover magazine, looking with concern at the growing governmental reliance on the polygraph, says the government is "starting in light of the fact that the tests are little more than sophisticated carnival tricks."

The machine the president sees as important to national security is what the magazine refers to as "an unreliable, pseudo-science thingamabob." Advocates of the machine counter that its accuracy is 95 percent. Leonard Saxe, a professor of psychology at Boston University and principal author of a 1983 study of the machine for the congressional Office of Technology Assessment, said, "It's a nice idea that, like Pinocchio, we all might give off some psychological indicator when we're lying. Unfortunately, we don't really know."

Saxe said that the "lie detector does work as long as the subject believes it works. A good examiner scares the crap out of you. It's theater." Shultz may see the extent to which the mystique of the machine can be carried. In the Washington Yellow Pages, one firm, Sting Security Inc., even claims it can detect lies by telephone. End Notes

Chicago talk show host Oprah Winfrey, who now finds herself an Academy Award nominee for her first movie role in "The Color Purple," isn't even her father's first choice for the Oscar. When asked about it, Nashville City Councilman Vernon Winfrey gave her costars the nod: "I think I'd put Whoopi Goldberg first, Margaret Avery second and maybe Oprah third." It might be pointed out that it was the first movie her father had seen in 25 years. Winfrey's Chicago show is an unqualified success and is even outdrawing Phil Donahue's show locally. And that's where Donahue was based for so many years . . .

Lady Bird Johnson was released from St. David's Hospital in Austin, Tex., yesterday. She had been there since Wednesday after fainting at the funeral of longtime friend and Austin newscaster Paul Bolton . . .

Mary Kay Quinlan, a Gannett News Service reporter, was inaugurated the National Press Club's second woman president Saturday. The 79th president, she was sworn in by Secretary of Commerce Malcolm Baldrige. The first woman president, Vivian Vahlberg, then a correspondent for The Daily Oklahoman, was sworn in in 1982 . . .

A scholarship in the memory of Christa McAuliffe has been established at Framingham State College, a school attended by McAuliffe, her mother and her brother. Gail Nolan, a former classmate of McAuliffe's there who is now working on an advanced degree at Georgetown University, said the scholarship will be awarded top teaching students at Framingham, which was the first state teacher's college in the country. The college is also planning to establish a building fund in McAuliffe's memory . . .