The first victim of the Gramm-Rudman-Hollings balanced budget law has been found in an unexpected quarter: It is House Democratic leader James C. Wright Jr. (D-Tex.), who fell from a makeshift platform while explaining the Gramm-Rudman-Hollings budget-balancing law and broke his left arm just above the wrist.

Undaunted, Wright showed up at the White House yesterday morning along with other congressional leaders. Wright joked that he had been "the first cut under Gramm-Rudman."

"The chair scoots out from under me and sequesters my arm," he quipped.

Marshall Lynam, Wright's administrative assistant, said that Wright will wear a cast for the next four to six weeks.

Lynam said that Wright was speaking to a group of about 35 "public-interest people, teachers, disabled veterans," at a reception Monday night and "standing on two chairs, with a foot in each chair."

"He stood up there about 15 minutes or so and answered questions dealing with the effects of Gramm-Rudman," Lynam said. "When he started to get down, he shifted his weight from one foot to the other and, when he did, one chair toppled over and he fell."

Lynam said that Wright, 63, tried to catch himself and put all his weight on his left hand, breaking his arm about an inch above the wrist.

At Walter Reed Army Medical Center, X-rays showed that the large radius bone was "broken completely" and the smaller ulna was cracked.

Lyng, Continued . . . Ever since John R. Block resigned as secretary of agriculture early this month, the name of former deputy secretary Richard E. Lyng has been on the lips of knowledgeable touts willing to discuss the likely nominee for the politically sensitive post. The word now, from both congressional and White House sources, is that Lyng's nomination is likely to be announced this week.

Lyng, a Californian, was almost tapped for the job in Block's stead five years ago, but Sen. Robert J. Dole (R-Kan.), now Senate majority leader, apparently intervened, pushing for a farmer and a Midwesterner. Said Lyng in an interview early this week, "I got Doled out."

Lyng served as California's director of agriculture when Reagan was governor, as an assistant secretary of agriculture under former president Richard M. Nixon, as president of the American Meat Institute and as Block's top deputy until a year ago, when he set up an agricultural consulting firm in Washington.

Easy-going, straight-talking, but somewhat colorless, Lyng is considered to be more politically astute and legislatively pragmatic than Block, although Lyng stressed in an interview Monday that "philosophically, John Block and I are peas in a pod."

Although Lyng seems to have surmounted political considerations this time, they have been as omnipresent in the past few weeks as they were in 1981. Congressional sources said that Vice President Bush, concerned about his presidential ambitions for 1988, had raised questions about the political wisdom of appointing a Californian to replace Block at a time when economic problems are far worse in the Midwest.

Also, Sen. Pete Wilson (R-Calif.) and a number of California farm groups had been pushing another candidate: John R. Norton, a California and Arizona farm operator who replaced Lyng as second in command at the Agriculture Department. Norton was said to have greater appeal among California's fruit and vegetable growers because he was sympathetic to their desire to employ what agriculture department euphemism calls "guest workers" from Mexico.

Three in Line . . . Another succession story unfolds at the State Department, where Otto Reich's nomination as ambassador to Venezuela will leave vacant the top spot at State's Office of Public Diplomacy, invented in 1983 to promote U.S. policy in Central America. Most lists of those who might be tapped for the job include three names: Col. Larry Tracy, who is Reich's deputy; Sam Dickens of the conservative American Security Council think tank, and Luis Aguilar of the Georgetown Center for Strategic and International Studies.