Four times in the past four weeks, three desperate women from Moscow stealthily penetrated the heavily patrolled Soviet-Finnish frontier area to wait on the shore of a remote lake for the arrival of a light plane to take them out of Russia to the man they love.

Each time, their clandestine-escape attempt was foiled by bad weather or bad timing. Now, the pilot of the aircraft has been arrested by the Finns after he was detected in restricted air space flying back from the Soviet Union in his rented Piper aircraft.

The woman - mother, wife and daughter of a Soviet defector - now await the arrival of the secret police.

This bizarre tale, including stealthy preparations, nerveless bluffs, bone chilling vigils in deep snow, and final shattering defeat was spun yesterday in a Moscow apartment by Ludmilla Agapova, a 39-year-old sailor's wife whose consuming desire to join her husband in Sweden has dominated her life for four years.

In her quiet, carefully controlled voice, Agapova laid out some of the details of her attempt to leave the Soviet Union after being insulted and fired from her well-paid job as engineer following her husband's sudden defection from his ship when it was docked in Sweden in 1974.

It is impossible to check any of her assertions about her foiled escape, but her husband's defection and the subsequent refusal of the Soviets to allow his wife, mother and child to join him is well known in Scandinavia. The Swedish government has made representations to Soviet leaders about the case without effect.

According to Agapova, this lack of response by the Soviets to either her entreaties or the diplomatic moves of the Swedes, who had granted her husband political asylum, forged in her mind the idea of flying out of Russia over the sparsely populated northern border.

The details she chose to recount have a ring of plausibility. Her mother-in-law, Antonina Agapova, 68, and her daughter, Lilya, 14, both agreed to the attempt. In January, Agapova traveled from her home in Kailningrad, near Moscow, to Leningrad, and then about 70 miles north to the small city of Priozersk, on the northwestern shore of Kake Ladoga.

From there, she traveled bu bus to a smaller lake near the shores of Lagoda, reconnoitering the rendezvous area numerous times and becoming familiar with ways to aviod detection. She found that the people of the area were vivilant and suspicious of any new faces, and that a complex series of internal permissions and official approvals was needed even to buy bus tickets ti the small towns of the area.

She checked the depth of the ice on the lake to ensure that a light plane could land and take off. A lake was decided upon because it was flat and clear of trees or other hazards. Once back in Kaliningrad, she communicated with her husband and soon the first attempt was ready.

The trio journeyed north to Priozersk. They faked their way past various officials, then got on a bus that would take them near the rendezvous lake.

The conductor asked for their permissions and tickets.

"We have them," Agapova lied.

"He didn't check to see," she said in an interview yesterday. "Not everyone works for the KGB."

Late at night, they got off the bus at a flimsy, open-sided shelter deep in the deserted countryside. They shivered through the night and slogged on foot to the lakeside to wait.

Dawn came, but no plane. It was March 11. They stayed out in the area through the following day for another arrival, but it was fruitless and theye returned to Kaliningrad.

More communications with Sweden; bad weather had stopped the flight. Gathering their strenght, they returned on March 19. Again, no plane arrived.

Once again, they were told, heavy weather had forced the lightly instrumented plane from making the flight. A final attempt was scheduled for April 1.

"It is horrible to remember," she said.

Pressed to the limits of their endurance, the three set out once again. But now, they found it nearly impossible to keep to the schedule they had set because the public transport was jammed with families returning from the annual spring school holiday. They arrived in Priozersk to find no room on the bus that would get them to the rendezvous of the rendezvous hour - 7:30 a.m.

The desperate women finally reached the lake an hour and a half later, their hopes frayed to breaking. Soring warmth had melted the thick ice. Twenty feet of water lay between them and the ice in the center of the small lake.

"We couldn't do it . . . We couldn't walk on water." Agapova said.

By that time, as nearly as she cana calculate, Finnish authorities had already detained Karl Goran Wickenberg and Per-Gunnar Nystrom at the Immolo airfield about four miles west of the Soviet border. According to reports reaching here, the Piper had dodged over the border and touched down briefly at a small lake inside Russia. Finding no one, the plane headed back, apparently across a restricted air zone, and landed in Finland, where Finnish police took the two Swedes into custody.

The three women, now in shock, went home once again.

"All attempts were in vain and have failed," Agapova murmured.

Two days ago, a Maj. Zubrikov of the Soviet secret police knocked at the door of Ludmilla Agapova. The major smoothly asked Agapova how she managed to support herself, a chilling question in a country where the much-trumpeted right to a job carries a grim double edge - not to work is a crime against the state. Agapova answered that she has a job cleaning lavatories.

The major never mentioned the trip to the unnamed lake north of Leningrad.