(CNN) -- The two little girls vanished nearly 40 years ago, their disappearance long faded from the public consciousness, their names etched in a stone marker their hope-sapped parents placed in a local cemetery.
But Maryland police have been tenacious about solving this cold case. And on Tuesday they breathed new life into it, when they announced a possible breakthrough.
Convicted sex offender Lloyd Lee Welch Jr., 57, who's been serving a prison sentence in Delaware since 1997, was near Sheila and Katherine Lyon on that March day in 1975 when they went missing, Montgomery County Police Chief J. Thomas Manger told reporters Tuesday.
Welch was at a plaza that was among the last places that the two girls were seen alive, and he was observed paying attention to the sisters, Manger said. He declined to state how police obtained this lead.
Manger said that anyone who has information about Welch should call authorities. Police released photographs of him and his now-deceased girlfriend, Helen Craver, about whom police are also seeking information.
"We need to know more about his activities," Manger said.
Welch, who also went by the name of Michael Welch or Mike Welch, worked as a ride operator for a carnival company that set up their attractions in malls around the country, Manger said. His girlfriend also worked at the carnival company.
Welch has "multiple convictions for sex offenses against young girls," Manger said.
Investigators believe Welch may have been involved in other unsolved crimes around the country. He was also a drifter and sometimes stayed in homeless shelters, Manger said.
Montgomery County police have stopped short of calling him a suspect in the two sisters' disappearance.
The case faded from the headlines years ago. If they're alive, the women would be 48 and 50 years old now.
After years of holding out hope, their parents gave up.
Sixteen years ago, they set a marker for their daughters in a cemetery with their dates of birth and the date they went missing, the Washington Post reported.
But the police department has not forgotten Sheila, who was 12, and Katherine, who was 10, the day their older brother, Jay Lyon, saw them last.
Maybe, in part, that's because he joined the police force as a homicide detective just a few years after that.
Walk to pizza parlor
The girls must have been full of anticipation when they decided to step out for some fun in their neighborhood not far from Washington, D.C.
Their birthday dates were just one day apart, and celebrations were coming up in just a few days. It was also the first day of Easter school vacation.
They walked half a mile to a nearby strip mall to check out the Easter decorations, the Montgomery Gazette reported.
Their mother told them to be home by 4 p.m. At 7 p.m., police received a call reporting them missing, the privately run missing persons website CharleyProject.org reported.
Police swarmed out looking for them and questioned passersby.
A medley of witnesses said they'd seen the girls. One saw them walking to the shopping center.
Another -- a child -- saw them talking to a stranger, a man holding a microphone and a briefcase. Police drew a composite of him based on the witness's description.
But the girls walked away from him.
An hour later, their brother Jay, 15 at the time, spotted them at the shopping center eating pizza. And after that, someone else saw them walking in the direction of their home, according to the CharleyProject description.
Had they arrived, they would have made it home on time.
Back then, it was common for children to walk to places in the neighborhood without their parents. But when the girls disappeared, that feeling of safety was shattered, the Gazette wrote.
The girls' father, John Lyon, was a well-known radio host in Bethesda at the time, so the story of his daughters' disappearance made the rounds.
Anonymous callers rang the family demanding money, CharleyProject.org claims. One of them demanded their father deposit $10,000 in a particular location.
He complied. No one picked up the cash. The man called again, but when asked for evidence that he actually had the girls, he broke off contact.
In the ensuing years, the tips faded. The case languished.
CNN's Michael Martinez and Dave Alsup contributed to this report.