The Grand Duchy of Luxembourg (pop. 360,000), often the recipient of American ambassadors whose political influence outweighed their diplomatic stature, has asked for and received something new - a professional U.S. diplomat.

The new ambassador to Luxembourg, informed sources said yesterday, will be James G. Lowenstein, deputy assistant secretary of state for European affairs. Lowenstein apparently got the job because Luxembourg took the advice of Sen. Claiborne Pell (D-R.I.) and asked the Carter administration for a professional envoy, not another political crony.

Pell, long a friend of Luxembourg and it royal family, suggested more than a year ago that the little country in the middle of Western Europe did not have to accept the cronies or financial supporters of American Presidents as ambassadors.

Luxembourg has seen a lot of them over the years, beginning with Perle Mesta, the Washington hostess whom Harry s. Truman sent there as ambassador after World War II. Dwight D. Wlenhower appointed Wiley Buchanan, a Texas millionaire and art collector, Richard M. Nixon sent Kingdon Gould, the Washington parking-lot magnate and contributor to the GOP, and then Ruth L. Farkas, who - with her husband - donated $300,000 to Nixon's 1972 reflection campaign.

According to reliable sources, Luxembourg took Pell's advice this year and quietly passed the word to the Carter administration that it would prefer an ordinary, professional diplomat as its next American ambassador. Luxembourg has a voice in this matter, since it is traditional diplomatic practice to offer a country the opportunity to reject a proposed ambassador if it finds the individual undesirable.

Pell said yesterday he could not discuss his conversations with officials in Luxembourg. But he acknowledged that he had told "individuals from small countries" that "if I were in their shoes I would not feel obligated" to accept a proposed ambassador "whom they felt did not bring to the job the prestige and dignity they thought their country deserved."

If confirmed by the Senate, Lowenstein will succeed Rosemary L. Ginn, 63, at St. Louis publisher and former Republican National Committee-woman. Gin took the embassy over from Farkas last spring.