Soviet authorities told the family of imprisoned dissident Anatoly Scharansky today to have a lawyer ready to defend him at trial in about a month.

The jailed man's mother, Ida Milgrom, 70, was told by authorities today, at the end of a six-hour interrogation at Lefortovo prison that "she may now look for a lawyer who could be neccessary in a month," according to dissident sources.

The notification is another step toward a potentially spectacular show trial in which American diplomats and possibly journalists will be accused of recruiting dissidents for U.S. intelligence purpose. Scharansky, a 29-year-old computer technician, was arrested March 15 by the secret police after a "repentent" dissident made such allegations against him.

He has been held virtually incommunicado in prison since then while the KGB questioned perhaps as many as 40 persons in an effort to build their case against the dissident.

The notification also constitutes something of a rebuff to President Carter, who has publicly and privately sought to persuade the Kremlin to release Scharansky and several over other major dissident figures from jail without trying them.

Scharansky applied to emigrate to Israel in 1973, but was refused on grounds that he knew state secrets. He then became a member of the unofficial group of human right activisits who were attempting to monitor Soviet performance on the human rights provisions of the 1973 Helsinki accord.

Acording to dissident sources, Mrs. Milgrom refused to give the questioners at her session today more than a "biography" of herself and her son, and she refused to sign a warning that if she divulged the contents of the interrogation she might suffer some penalty later. She also told the authorities that her family had retained a French lawyer to defend her son.

She was told it was impossible for a foreign lawyer to participate," said a source. "She was told to find a lawyer from the Moscow collegium of lawyers."

Her husband, Boris Scharanksy, 73, and another son, Leonid, 32, were told to report to Lefortovo Thursday afternoon for further questioning. Anatoly Scharansky reportedly faces a charge of treason, a capital crime.