President Reagan intends to nominate Lilla Burt Cummings Tower, an attorney and the wife of Sen. John Tower (R-Tex.), for the position of director of the Institute of Museum Services, an agency the Reagan administration had earlier recommended closing down.

Reached yesterday, Tower said she still must be confirmed and that she was busy working on a case and "winding up a law practice."

Tower, 52, was assistant to the chief economist at the Rand Corporation from 1950 to 1953. She has been in private law practice since 1960, the year she graduated from George Washington Washington University with a law degree, according to a White House press release. She received a master's in law in 1965, and in 1973 she was appointed by then-Mayor Waltor Washington to the D.C. Board of Zoning Adjustment.

Lawrence Reger, director of the American Association of Museums, commented on the nomination of Tower: "I feel very good about it. It shows an intention to seriously consider the IMS. The administration had recommended only about half a million [in fiscal 1982] to wind it out. I'm assuming that they would not appoint a director of her stature if they expected the agency to be wound out."

Since then, the House Appropriations Subcommittee on the Interior, chaired by arts supporter Sidney Yates (D-Ill.), has recommened a budget of $14.4 million for fiscal 1982 to keep the agency going.

Tower apparently has no museum work background. "I hear she and Sen. Tower have a personal interest in museums and follow what's going on," said Reger.