Independent counsel Lawrence Walsh deserves the absolute support of Congress and citizens for his determined efforts in the Iran-contra investigation {"Walsh Vows to Pursue Probe to End,'' June 18}. The Justice Department's attack on the office of the independent counsel can only be described as transparently self-serving. It appeared that the Reagan administration might yet again succeed in getting Congress, the media and the judiciary to back off in the face of its overrated public popularity.

This administration operates with contempt for the public and Congress and skillfully uses the media as its sometimes unwitting, sometimes very willing, partner.

I support Mr. Walsh's investigation, and it is my hope that he leaves no stone unturned to get to the complete truth. Contrary to those who think it is bad for the country for the investigation to drag on, I believe that in the long run a cover-up or an incomplete investigation holds far more serious consequences for the integrity of our government.

As for the dangerously complacent who get upset only when their afternoon soap operas and game shows are preempted by the Iran-contra hearings, I surmise that they are living in the same fantasy world as the president and don't want to know the truth any more than he does; he has them just where he wants them. KATHERINE D. WELLS Arlington