The 31-year-old star was seen kissing Dominic, 50, despite the fact he is supposedly happily married to wife Catherine Fitzgerald.
Lily and Dominic shocked onlookers as they enjoyed a meal together in Italy, while also being unable to keep their hands off each other.
However, days later The Affair star then put on a united front with his wife, insisting their marriage was "strong" and they are "very much still together".
In an interview with Harper's Bazaar last month, Lily was promoting her new movie Rebecca when she spoke about affairs, her rebellious streak and how she makes mistakes often.
Lily, who is shooting The Pursuit of Love with Dominic, said, "I feel I've rebelled in that way, I was always a rebellious teenager and I think it's important for us to rebel all the time."
"I think criticism can be good if it's constructive but I feel like if it's attacking you or a vendetta that's really difficult but I'm still learning."
"I'm still figuring it out but I do think I can grow and develop a thicker skin. All that really matters is how you feel about yourself and how the people you love feel about you, that's the truth."
On mistakes she said, "I think I make mistakes all the time, that's what life's about and I would never want to run away from a situation or be too scared to act...
"I think it's better to throw yourself in and make mistakes with an open heart. If your instincts are right even if they're misguided or if you're open you can recover from your mistakes and learn from them."
Speaking about her new movie, she said, "The character of Rebecca went against all norms as a woman, disobeyed her husband and had affairs was basically just brilliant and that was only in the 1930s and people are afraid of women when they're unleashed and women are warriors and that's intimidating."
Lily also added that she wishes her younger self "had not been so obsessed with boys" and that she often wants to be "another person".
Dominic shares four children with Catherine: daughter Dora, 13, son Senan, 12, son Francis, 11, and daughter Christabel, seven.
The pair showed they were very much still together by addressing paparazzi outside their home on Tuesday, telling reporters, "Our marriage is strong and we're very much still together."
According to Daily Mail, Catherine appeared anxious during the whole situation, keeping her hand in her pocket, hiding her ring finger and also carrying a wadded-up tissue.
A friend of Catherine's told the publication she was "devastated" when she saw the pictures as she believed she and Dominic had a "good marriage".
They added that she considered the marriage to be "probably over".
"She is privately fuming. There are some difficult conversations to be had, but those will take place behind closed doors. For now she was happy to display a show of unity and will always put her family first," the source said.
Friends told the publication the photo-call was "definitely Dominic's idea".
Lily and Dominic have known each other for some time and also worked on Othello together in 2011, a year after he married his wife.
Lily recently parted ways from her on again off again beau of five years Matt Smith of The Crown fame after the pair seemed to attempt to rekindle their romance during the UK’s lockdown period.