Lilla Tower, who has provoked controversy as director of the Institute of Museum Services, resigned late yesterday, the White House announced.

Tower, the wife of Sen. John Tower (R-Tex.), wrote in a letter to the president that she was "reluctant to depart from this administration which I am so privileged to serve . . . but ever increasing demands made on my husband and me by this forthcoming campaign for reelection to the Senate make it imperative that I now be free to devote my undiminished time and energies to this campaign and this effort."

Her resignation is effective Tuesday, and there was no word late yesterday on whether an acting director has been named. Tower spent the day in a closed meeting of the IMS board that was devoted to examining grants.

The institute provides general operating support to museums of all types, ranging from art institutes to zoos and botanical gardens.

Tower, a lawyer, came to her post two years ago with no previous experience in museum administration. During her tenure she has caused exasperation and discontent among museum officials and advocates who said they found her quirky and difficult to deal with. Last year she disqualified because of incompleteness more than 65 funding applications from museums. Museums and lobbyists claimed in outrage that the missing parts were technical, not substantive, omissions.

"She never participated in any events in the museum world," said Craig Black, the director of the Museum of Natural History of Los Angeles County, who sits on the board overseeing IMS. "There was almost a total absence of her or her staff at meetings of the museum world, whereas the National Endowment for the Arts and the National Endowment for the Humanities were always represented.

"It was difficult for museum professionals to know what she was really thinking and what her plans were for the museums," he said. "There was no dialogue."

Many IMS staff members have left during the last two years, and not all of them were replaced, because Tower was trying to streamline the agency.

"You can't have an agency that is turning over personnel at that rate," said Black. "It's been practically a revolving door."

As one of President Reagan's appointees, Tower followed the party line, even when it meant asking Congress to phase out her own agency. That was Reagan's request and she supported it two years in a row as she went to the Hill to face Rep. Sidney Yates (D-Ill.), chairman of the House Appropriations subcommittee that funded her agency. But each year Yates included money in the budget for IMS.

This year Tower brought before the subcommittee a White House recommendation that the agency be maintained at a budget of $11.5 million for fiscal year 1984. Yates' subcommittee is recommending $21.5 million.

She also proposed that museums receiving challenge grants from one of the national endowments be disqualified from also receiving IMS grants. The American Association of Museums opposed that move and so did the House in its appropriations legislation.

As an example of Tower's feelings about funding, she said in a Dallas Times Herald interview last December: "Why should the miner, extinguishing his life in the coal mines, subjecting himself possibly to black lung, pay . . . basic costs for museums with his tax dollars, when life is hard?"

Yesterday, Reagan, in his letter to Tower, applauded her cost-cutting measures.

"To your credit," Reagan wrote, "you have guarded against making museums dependent upon federal government largess or hindering them needlessly by bureaucratic red tape. Your strong management has effectively streamlined its operation and enhanced its productivity."