Dominic, who turns 51 on Thursday has been filming an adaptation of Nancy Mitford's novel with Lily in the U.K. over the summer, but they were pictured looking intimate while on a trip to the Italian capital in snaps obtained by Britain's Daily Mail newspaper.
In the pictures, they are seen sharing an electric scooter, while he places his hands around Lily's waist and in other snaps he appears to give kiss her neck and tenderly touch her hair while sitting at a table outside a restaurant.
"The Affair" star is married to aristocratic Irish landscape gardener Catherine FitzGerald, with whom he has four school-age children. The couple has not announced any split. He also has an adult daughter from a previous relationship.
The "Baby Driver" actress reportedly ended things with on-off beau Matt Smith recently after dating for more than five years, after a failed attempt to rekindle a romance they called a halt on in December.
A source told British newspaper The Sun of their split, "They have gone back and forth this year trying to sort things out between them because they both have so much love for each other."
"But unfortunately it just isn't working and they have mutually decided to just close this chapter of their lives."
Dominic and Catherine have been married for ten years. Both their representatives have been contacted for comment, but did not immediately respond to the request.