"She is a sweet woman and we talked about how she spends her weekends, houses and music. She is really cool," Mr Hamilton said on last night's Graham Norton show.
A spokesman for Debrett's, the society etiquette experts, said: "The Queen would begin to speak to the person on her right, the guest of honour - for the duration of the first course."
It is not known who was the guest of honour at the lunch.
Debrett's added: "For the next course she would speak to the person seated to her left. This thus indeed means it is convention at a dinner party to speak to the guest seated to one's left before speaking to the one on the right - also with the Queen.
Etiquette expert Major General James Cowan says the convention encourages flowing conversation.
Watch: Lewis Hamilton discusses meeting the Queen on Graham Norton
"The hostess will begin conversation with the guest seated on her right. The other women should follow suit. Halfway through dinner the hostess will direct her conversation to the guest on her left and the guests should do the same," he said.
Mr Hamilton is not the first high-profile figure to struggle to meet the Queen's high expectations.
Michelle Obama, wife of the US President, fell afoul of strict Royal protocol during a state visit to Britain in 2009 when she hugged the Monarch during a photo call.
Five people are known to have publicly broken the unwritten 'no touching' rule.
German officials were issued a four-page guide to royal protocol ahead of this week's state visit including a strict injunction against trying to take a 'selfie' with Her Majesty.
Former US President George W. Bush invited a scathing look from the Queen when he suggested that the 89-year-old Queen had been on the throne since the 18th century.