THE FIRING of Rita Lavelle is closely connected to all the other troubles into which the Environmental Protection Agency has fallen. President Reagan's curt dismissal of Miss Lavelle is a highly visible but minor aspect of the agency's lamentable performance in enforcing the law on poisonous waste dumps.

We would not want to leave you under the impression that we fully grasp the internal politics of the EPA in its current decline. It is not easy--and perhaps not possible--to disentangle the questions of public policy from the sheer managerial incompetence and the venemous personal vendettas that currently characterize it. But it all revolves around the Superfund.

Congress created the Superfund two years ago to give the EPA the money as well as the authority to clean up dangerous dumps of waste chemicals. The cost of the cleanup was to be retrieved by suing the dumpers. President Reagan was not against the principle of the thing. The bill was still moving through Congress at the time of the 1980 election, and it was finally passed only after the president- elect gave his assent.

But under the new administration, prosecution of chemical waste cases slowed down sharply. Instead of using Superfund aggressively to clean up dumps fast, the EPA shifted to a strategy of negotiating with the dumpers. People in Congress began to complain that the EPA was settling these negotiations on terms too favorable to the companies. Miss Lavelle was in charge of waste enforcement. Shortly, two House subcommittees undertook investigations. When the agency's administrator, Anne M. Gorsuch, refused to provide them with documents that they sought, the result was the vote to prosecute her for contempt.

Meanwhile, Miss Lavelle had run into further embarrassment in her attempts to shut up a whistleblower in the agency who had been talking to outsiders about toxic waste. Still another House subcommittee held hearings on the whistleblower case, and the chairman later said that he was inclined to ask the Justice Department to prosecute her for perjury.

On Friday, the EPA said that Miss Lavelle had resigned. Over the weekend she said that she hadn't. Since she was a presidential appointee, the president could fire her. And, on Monday, he did.

While the Lavelle case has certain aspects of soap opera, the poisons in those dumps are real and they are dangerous. The president needs to go further than firing one appointee. He needs to put the agency in the hands of people who can run it efficiently, people who know that their job is not ideological jousting with the House Democrats but providing effective protection to the public health.