Independent Counsel Lawrence E. Walsh yesterday named Andrew L. Frey, a former deputy solicitor general, to argue the key appeals in the Iran-contra convictions of former White House aide Oliver L. North and former national security adviser John M. Poindexter.

Walsh, who is attempting to wind up his four-year investigation into the Reagan administration's longest-running political scandal, believes sustaining the convictions is important not only for his own inquiry but also to avoid the precedent that reversals would set, sources said.

Frey, 52, served in the solicitor general's office of the Justice Department for 14 years and has argued 60 cases before the Supreme Court, according to Walsh's statement.

North's three-count conviction -- for altering and destroying official documents, aiding and abetting the obstruction of Congress and accepting an illegal gratuity in 1989 -- was set aside by the U.S. Court of Appeals for the District of Columbia last July.

The court, in its decision, set a new standard for prosecutors in cases where defendants such as North and Poindexter have testified before Congress under limited immunity in widely publicized hearings.

In North's case, the appeals court determined that the trial judge should have ordered a witness-by-witness and line-by-line review of grand jurors who voted to indict North and of witnesses who testified at his trial, in order to determine if their views were influenced by North's immunized testimony.

Walsh has decided to appeal that decision to the Supreme Court, sources said.

Poindexter, who was found guilty on five counts last April, filed his appeal on Dec. 14 with the same court. His lawyers cited the North appeals court decision, asserting that immunized testimony also may have been a factor in his case.

Poindexter appealed his conviction on specific counts relating to his making false statements to members of Congress about aid to the Nicaraguan contras and arms shipments to Iran. His attorneys argued in part that "it is not a crime to make evasive, potentially misleading, but literally true. . . unsworn statements to Congress in an effort to influence a legislative inquiry."

Referring to Poindexter's failure to discuss frankly the covert arms sales, the appeal petition said, "Secrecy always surrounds covert actions, and the need to preserve secrecy frequently has led prior administrations to resort to deception and, in many instances, outright lies . . . . But never before had such conduct resulted in prosecution."

"Congress," the petition said, "has ample other protections against falsehood; it did not intend to interject the threat of criminal prosecution into private discussion between representatives of the political branches, especially where, as here, no oath is administered and no verbatim transcript is maintained."

Walsh has yet to respond to the Poindexter appeal, but oral arguments in the case are scheduled for Feb. 28.

Frey, who will be paid on a per-diem basis, is a partner in the Washington office of the Chicago-based law firm Mayer, Brown & Platt. In November 1988, he argued before the federal appeals court on behalf of former White House aide Lyn Nofziger, who had been convicted of illegal lobbying after an investigation by another independent counsel, James C. McKay. In June 1989, the appeals court overturned Nofziger's conviction.

In a related matter, U.S. District Judge John F. Keenan decided in New York that he will address the question of whether a former employee of Walsh, Jeffrey

Toobin, used grand jury secrets in a manuscript that Toobin is attempting to publish about his experiences working for the independent counsel's office in the North case.

Walsh has objected to publication of Toobin's book and wants Chief U.S. District Judge Aubrey E. Robinson Jr. to rule on the issue, because Robinson surpervised the Iran-contra grand juries.

Keenan said yesterday it would be a waste of judicial resources to send part of the case to Robinson in Washington. Instead, Keenan decided that he would deal with the grand jury matter at a previously scheduled Jan. 3 hearing in New York.