The judge in Lyn Nofziger's trial yesterday questioned whether prosecutors had proven an essential element of the allegation that the former presidential aide illegally lobbied Edwin Meese III for Wedtech Corp. when Meese was on the White House staff.

U.S. District Court Judge Thomas A. Flannery asked the prosecution to cite evidence that Wedtech's bid for a defense contract was of "direct and substantial interest" to the White House when Nofziger wrote a memo to Meese, then presidential counselor.

The judge, who reserved decision on the issue, expressed dissatisfaction with the answers he received from independent counsel James C. McKay while the trial was in recess for legal arguments.

"I am asking for the evidence showing the direct and substantial interest of the White House as to this particular contract," the judge said during a hearing on defense motions for directed verdicts of acquittal.

The charge that Nofziger wrote an April 8, 1982, memo to Meese is one of four counts in the indictment charging illegal lobbying by the former White House political director.

Nofziger's lawyers contend that the prosecution failed to prove such White House interest on any of the three issues that Nofziger is accused of contacting former colleagues about in 1982.

The trial is set to resume this afternoon, when the defense is scheduled to begin presenting its case.