The 74-year-old musical theatre impresario told Huw Edwards on BBC News about the occasions on which he was given the "great honour" of entertaining the Queen, including when she visited his home.
Lloyd Webber said he received the visit of the Queen in 2012, when he co-wrote Sing with Gary Barlow — which ultimately became a number one single for Barlow alongside The Commonwealth Band and Military Wives — to mark her Diamond Jubilee.
Lloyd Webber said he invited the Queen to his home for an informal performance of the track with a choir he assembled.
"We put together a choir of racing people, because the Queen's love of racing we all know," he said.
"I won't say it was the best choir that I've ever had, but we put that together and sang the song for her. She was wonderfully generous about it."
Lloyd Webber said the "lovely evening" also featured performances — including by Wild Rose star Jessie Buckley — of several Rodgers and Hammerstein numbers, reflecting the Queen's "great love" of the duo since childhood.
He stated that he had become able to know the Royal Family over the years, partly as a result of Prince Edward coming to work for his theatre company in the 1980s.
The theatre star added: "Over the years, I've got to know her a little bit off-duty. She was always the Queen, but it was quite wonderful to have the occasional chat with her — sometimes the odd disagreement even.
"One of the things I was quite amused about is she didn't share my love of Victorian architecture."
Turning his attention to Monday's funeral for the Queen, Lord Lloyd-Webber said it was an "absolute privilege" for him to be able to attend.
He added: "It is really a day where we all have to, I think, reflect on one of the most remarkable women that anybody will ever see.
"She represented stability at a time when there has been so much change and, I think, the outpouring we have seen in the last week ... I have been in New York actually and it's extraordinary how even there it has deeply, deeply touched people.
"All I can say is that I feel very, very, very lucky and privileged to have actually met what has to be probably the most remarkable woman of the past 50, 70 years. What more can one say?"
Lloyd Webber was made a Knight Bachelor by the Queen as part of her Birthday Honours in 1992 and became a life peer five years later.
In 1992, he started the Andrew Lloyd Webber Foundation, which seeks to promote British arts and cultural heritage.
Watch: Andrew Lloyd Webber remembers Queen Elizabeth II