THE DISPUTE over President Reagan's decision to unseat a Carter administration appointee to the District's Judicial Nomination Commission has serious implications for the quality of the city courts. Mr. Reagan asserted a right to have his own appointee on the board last week by naming Philip Lacovara to the position. He did this even though William A. Borders had been appointed by President Carter to the same position in 1980 for a five-year term. Both Mr. Lacovara and Mr. Borders are respected lawyers who would probably do good work on the commission. But only one man can hold the commission's White House seat. Mr. Borders says he will file suit to prevent Mr. Lacovara from replacing him, and he has Mayor Barry's public support. Meanwhile, Mr. Lacovara and Mr. Reagan argue that the president has the right to have his personal representative on the commission.

Mr. Border's position is that presidential appointments to the commission do not change with administrations. The statute creating the commission sets the presidential appointment for a five-year term. That apparently is without regard to the person who comes to or leaves the White House. The president believes that he is within his rights to have his own man. In fact, the commission is intended to be representative: the president, the city council, and the chief judge of the U.S. District Court each appoint one person; the D.C. Bar and the mayor appoint two.

The Judicial Nomination Commission picks nominees for the D.C. Superior Court and the D.C. Court of Appeals. It gives a list of its top three candidates to the president, who then selects one person for each vacant judgeship, subject to confirmation by the Senate. In this process the president, obviously, has the final say in most cases, since the Senate rarely challenges his choice. Nevertheless, the president must pick one of the three candidates offered him by the commission and for that reason he values having an appointee on the commission to help craft the character of that list.

The Judicial Nomination Commission was set up as a non-partisan group, and it ought to be left that way. The intention was that the White House appoint a first-class legal mind to the group, rather than that the president appoints someone of his own party or persuasion. If the city is to have the best judges, no appointee to the commission should be under obligation or pressure to select a candidate for any reason other than that the candidate would make a fine judge. There are major arguments to be made for letting the mayor make the final choice for local judgeships instead of the president. These are local court judgeships, after all, and should be the full responsibility of the local government.