A House subcommittee investigating Rita M. Lavelle's management of the Environmental Protection Agency's hazardous waste cleanup fund issued her a subpoena--"not an invitation, not an RSVP"--and Lavelle "didn't show," a U.S. District Court jury here was told yesterday.

Defense attorney James J. Bierbower countered by saying that Lavelle "did nothing sinister or willful" and that "everything was a product of a misunderstanding."

The statements came as Lavelle went on trial before a jury of eight women and four men. She was indicted in May after the House voted, 413 to 0, to hold her in contempt of Congress for failing to respond to a subpoena issued by the House Energy and Commerce subcommittee on oversight and investigations in its probe of management of the EPA's $1.6 billion "Superfund."

Assistant U.S. Attorney Timothy J. Reardon III said that, from the time Lavelle received the subpoena Feb. 23 "until this day," she "did not pick up the phone, write a letter or send a messenger" to tell the committee that she was "under duress, hospitalized or kidnaped" and could not appear.

Bierbower said that Lavelle, whom he described as a "young woman whose world collapsed on her almost overnight" during the "shake-up at the EPA" had testified numerous times to various committees investigating management of the fund. President Reagan fired her Feb. 7.

At the time of her scheduled subcommittee appearance, he said, Lavelle was ill in California with a polyp in her throat that she thought might be cancerous. He said she was out of a job, "practically broke" and could not afford to fly here to testify without receiving some funds from the panel.

"She did not have the wherewithal and the health to make it this one time," Bierbower said.

John D. Dingell (D-Mich.), chairman of the Energy and Commerce Committee and the subcommittee that initiated the contempt action, testified for more than 90 min- utes yesterday as a prosecution witness.

In response to Reardon's questions, Dingell said neither Lavelle nor her attorney notified the committee that she could not testify last March because of health or financial problems.

Questioned by Bierbower, Dingell said that, had Lavelle told him she needed funds to travel from California to testify, he would have been "moved strongly" to grant such funds.

The prosecution rested its case after presenting two House staff members who testified that they gave Lavelle the subpoena.

Bierbower told reporters later that he expects Lavelle to testify today. He said that he will also call Lavelle's father, her physician and one of her friends and that defense arguments will probably conclude today. If convicted, she faces a year's imprisonment and a $1,000 fine.

A federal grand jury also is investigating whether Lavelle and other former EPA officials committed perjury during congressional testimony.