Lynne V. Cheney is getting to be hard for educationists to live with. Last November this troublemaking woman blasted the whole educational establishment for its "tyranny" in producing miserable textbooks. Now she has further embarrassed the establishment by inquiring into the testing of high school students abroad. What will she do to discomfort us next?

Cheney, for the record, is chairman of the National Endowment for the Humanities. A few days ago she released, without comment, the texts of examinations given to students in France, Germany, England, Japan and the European Community. Her silence spoke louder than words.Without rubbing it in, the chairman made the point that America's young people will grow to adulthood in a world of international competition. They will face a much higher level of intellectual demands than we have known before.

In England, by way of example, all 16-year-olds (our 10th-graders) take a general examination on their academic achievements. Then about half of them begin a two-year college-preparatory program (the equivalent of our 11th and 12th grades) leading to a second examination when the students are 18.

By way of example, England's 16-year-olds may be asked to answer questions about the Gunpowder Plot (if it was a plot) of 1605. A comparable question for our 16-year-olds might deal with the treason (if it was treason) of Aaron Burr. The questions cannot be answered by guessing at multiple choice selections or by marking true or false. These 10th-graders have to look critically at conflicting evidence.

The student in England who is college bound takes the second examination two years later. Some questions deal with U.S. history. Try these for size:

- "Why, and with what justification, is the presidential election of 1800 spoken of as a `revolution'?"

- "Assess the extent and significance of opposition to Western expansion in the pre-Civil War period."

- "Account for the prominence of the temperance issue in American politics from 1900 to 1933."

Would our college-bound high school seniors have an equivalent knowledge of British history over a span of 200 years? Cheney wonders about this. All of us ought to wonder.

Or take the examination given to college-bound students in Japan. Here a student is quizzed not only on Japanese history and culture, but on the history of England beginning with the Vikings. A typical question deals with commerce between France and England in the time of Louis XIV.

In France, the college-bound student may be examined in Russian literature. A moderately difficult question asks for an essay contrasting presidential power as it has been exercised by U.S. presidents since Truman. Yet another question deals with debt management in the Third World.

A German student may be tested on "the role and significance of Robespierre in the French Revolution." This same student is expected to have an intimate knowledge of the Weimar Republic. Would our high school seniors have "mastered an equivalent knowledge of U.S. political history in the 1920s?"

Cheney's purpose in releasing this sobering comparison is to promote national achievement testing here at home. She believes this can be done without resort to a nationally prescribed curriculum - something most conservatives would fiercely resist. She also believes a standard test can be put together fairly for all students and not merely for those going on to college.

All of this amounts to a tall order, but if 18-year-olds abroad can handle tough questions, our own young people had better be prepared to handle equally tough ones here at home.