Jackie shot to fame for the way she handled a chaotic parish council meeting, in which participants were seen losing their cool and trading insults.
The impresario released a song, on Instagram, about the Shropshire-based chief officer of the Cheshire Association of Local Councils.
And he told Good Morning Britain: “When you’re bored, you have to think of things.”
He said of the parish council meeting: “It’s sort of operatic.”
The composer plays the piano and Carrie Hope Fletcher sings, with the lyrics of the new song written by Don Black.
“It was just a laugh, I was doing nothing on a Sunday afternoon,” Lord Lloyd-Webber told the ITV show.
“At the moment. the Americans think I’m stark raving mad because they heard this song. They are saying ‘Who on earth is Jackie Weaver?'”
A friend from New York called “last night and woke me up and said ‘Who is Jackie Weaver?’ and I said ‘Well, it’s a very British thing’.”
He joked of the prospect of turning the song into a West End musical: “You never know! People said Eva Peron (Evita) was a bad idea.”
Jackie, who lives in Prees, north Shropshire, became an overnight internet sensation after she kicked Handforth Parish Council chairman Brian Tolver off the Zoom call after he told her to “stop talking”.
Lord Lloyd-Webber also discussed taking part in trials for the Oxford coronavirus vaccine and being told afterwards that he had had the real jab and not the placebo.
“I guessed I might have done … I was around people who got it (coronavirus) in the period after the last lockdown and I absolutely didn’t,” he said.
“I had no effects from the trial whatsoever, I felt right as rain.”
He was told, after a different blood test recently, that he has “got so many antibodies”.
“It’s very encouraging to think… eight months later, I’m teeming with antibodies,” he said.
He described the post-Brexit red tape affecting musicians and other artists as “crazy” and said of theatres remaining closed in the pandemic: “It’s all very worrying… We are all running out of petrol.”