The Homeland actor and The Kills frontwoman were spotted cosying up together at private members’ club The House of KOKO’s summer party on Wednesday evening, the latest in a series of high-profile outings the couple have been seen at together.
In recent weeks, the pair have also been seen together at the National Gallery's inaugural summer party, the Serpentine Summer Evening event, and the British Formula One Grand Prix at Silverstone.
Mosshart, who originally hails from Florida, is best known as a lead vocalist for The Kills and The Dead Weather.
According to her mother, Vivian, the pair met through mutual friends in London.
“I don't know how much flak I'm going to get for all of this but of course we are excited for her,” she told the Daily Mail.
“They have mutual friends. I don't know exactly how they met but I'm fine with it. If she's happy, we are happy. I'm yet to meet him but certainly I'd like to.”
When asked to describe the musician, she replied: “She's not an easy one to sum up. She's a complicated, beautiful lady, and very intelligent.
“She's so very talented in so many areas that it constantly surprises us. It amazes us, actually. We are very proud.”
The news comes 15 months after 51-year-old Lewis was left devastated following the death of his wife, actor Helen McCrory, from breast cancer at the age of 52.
The couple married in 2007 and shared a daughter, Manon, 15, and a son, Gulliver, 14.
Prior to her death, McCrory said she wanted Lewis to have “lots of girlfriends”.
She added: “You must all love again, love isn't possessive, but you know, Damian, try at least to get through the funeral without snogging someone.”
In June, Lewis said that his late wife was “still with us”.
Speaking on Good Morning Britain, he described her as “a fabulous human being” who had an impact on “people from all walks of life”.
The Independent has contacted Damian Lewis’ representative for comment.