Harrison even wrote a song for him, "Sour Milk Sea," that was released as a single, and that went nowhere too.
But Lomax, who played numerous concerts in the Ojai area where he'd lived in recent years, seemed to take it in stride. And he was not about to judge his career in music on the time when he was backed by members of the Beatles.
"Trying to cash in on that," he said in a 1980 interview with The Times, "would be like trying to stretch a string a mile. I'm English — I can't just go around telling people how great I am."
Lomax, 69, died in his sleep Sunday after a brief illness at the family home in the Wirral, a peninsula in England across from Liverpool, according to a statement released by his family.
The son of a millworker, his rock 'n' roll career ebbed and flowed even more than most in entertainment, from being signed by the Beatles' Apple records, to the point that he took restaurant jobs between gigs. But he said that was all part of the music life.
"This is what I picked," Lomax said. "You just have to accept, as I learned a long time ago, that you won't be busy and hyper-successful all the time. There are cycles when things are up and cycles when things are down, just as in life."
Jackie Lomax was born in the Wirral on May 10, 1944. He first gained notice as the vocalist and bass player with a band called the Undertakers, which was part of the Mersey Beat movement that swept England and other parts of Europe in the early 1960s. The band — which dressed in dark suits and black top hats, and had skulls and crosses painted on the amplifiers — scored high in popularity polls and played numerous times in the famed Cavern Club in Hamburg, Germany.
But it was another band that played the Cavern, the Beatles, that rocketed to fame, and the Undertakers broke up. Lomax's next big break came in 1966 when singer Cilla Black saw him at a party and told him that the Beatles manager, Brian Epstein, was looking for him, according to "The Ultimate Beatles Encyclopedia" by Bill Harry.
Epstein died the next year, but the Beatles label, Apple, signed the singer. Harry said the failure of Lomax's records "completely baffled the Beatles because Jackie had one of the rare and distinctive voices which have the potential of turning its owner into a superstar."
Lomax came to the U.S., where he formed bands, did more recording and took jobs to get through the bad times. Los Angeles producer Saul Davis said Lomax was the maitre d' at the Hollywood restaurant the Cat & Fiddle when Davis and his wife had their wedding reception there in 1987. "He needed to earn a living," Davis said. "He seemed OK with being there." In 1990, Davis co-produced an album featuring Lomax singing the Tim Buckley song, "Devil Eyes."
Lomax played session dates, toured as a backup musician and performed in mostly small clubs for the rest of his career. He was married to the former Norma Kessler, the mother of fashion photographer and music video director Terry Richardson. She died last year.
Lomax is survived by three daughters from his first marriage to Dionne Lomax and five grandchildren. He had returned to England in July to attend the wedding of one of his daughters and stayed until his death, according to Alistair Hepburn, the Lomax website manager.
At the time of his death, according to the site, the singer had recently finished a new album titled "Against All Odds."