Sonja drew a pink heart over the two in the photo which she captioned: "2years 2day."
Lorde also posted a photo on Instagram of the pair together, captioning it: "two years, and sandstorms, and the stars haven't left my eyes".
Early last year, Lowe wrote about his experiences in dating Lorde since her transition to a pop superstar and how it has affected him on his blog, Ono Field.
"My life is probably a lot different now," he admits. "But it feels normal on the inside.
"While I'm not the center of attention here (and f***, the times I have [been], it's never been fun), I do become aware of the people around me and their transparency."
Meanwhile, Lorde celebrated a different family occasion earlier this week as she took to her photo app to wish her father, Vic, a happy birthday.
The Kiwi songstress posted a flashback photo of herself with her dad in which she shared some kind words about him.
"Big happy birthday to the coolest customer there is: VIC! love you so much, dad. thanks for everything you do,' penned the Grammy Award winner.
- Daily Mail