The Smile singer shared a pic of the actor - or rather his bulging biceps - which she captioned ‘Mine’.
The Instagram post comes just a day after Lily and David - who plays Hopper in the Netflix show - were spotted kissing on the street in New York.
As well as their PDA in NYC, the couple have been seen together on a number of occasions over the last few weeks, including a date night at the Hughie Fury vs Alexander Povetkin boxing match at London’s O2.
Lily also supported the 44-year-old star during his Saturday Night Live hosting debut at the weekend.
David was previously dating Fantastic Beasts star Alison Sudol, but the couple split earlier this year following a long-term romance.
Prior to that he dated Riviera star Julia Stiles for four years between 2011 and 2015. Before this, he was engaged to Forgetting Sarah Marshall actress Maria Thayer.
Lily separated from husband Sam Cooper in 2015 after almost four years of marriage. The couple - who have two daughters - divorced in 2018.
They now share joint custody of Ethel, seven, and Marnie, six, and remain friends.
In January, Lily announced that she and her boyfriend of three years, Meridian Dan, had split up, claiming it marked the first time she’d been single since her teenage years.
She explained: “I’ve always had a boyfriend. I don’t, at the moment. I’m single, for the first time since I was about 15. We’ve been broken up for about three weeks.
“I’ve just come back from a tour in America, which is where I was when things went wrong with Sam [Cooper], and the same thing happened in my current relationship.”
Referring to her behaviour on her Sheezus tour, which she recently documented in her autobiography, Lily quickly added: “I mean, I didn’t take lots of drugs and have lots of sex with other people. I just became very lost.
“It’s been bad news after bad news and the fact that I haven’t called him and been like, ‘Can you come round for a cuddle?’ is big for me, because ordinarily, when things get difficult, I do need to have somebody around to share those problems.”