Avril Lavigne Sparks Buzz Stepping Out (and Skateboarding!) with Country Singer Nate Smith

She was a punk and he was a country singer — what more can I say?

On Tuesday, Avril Lavigne and Nate Smith sparked buzz when they were spotted stepping out for dinner at Catch in Los Angeles.

In photos, the "Bois Lie" singer, 39, and the "Whiskey on You" performer, 38, were seen stepping out of the restaurant in all-back ensembles. In photos obtained by TMZ, the pair was also spotted skateboarding around following dinner.

According to a source, however, the pair is not dating.

Instead, "they are discussing a music project together," the source tells PEOPLE exclusively.

A rep for Smith did not respond to PEOPLE's request for comment.

The buzz comes after a source confirmed to PEOPLE that Lavigne had ended her whirlwind romance with Tyga for good in October. They had dated on and off since February 2023.

Earlier this month, Lavigne announced dates for her first-ever greatest hits tour, set for 27 dates across North America with opening acts All Time Low, Simple Plan, Girlfriends and Royal & the Serpent appearing throughout the run.

"Tour dates for 2024 baby! I’ll be doing the Greatest Hits from all of my albums and along with some of your favorites, perhaps some special requests?" wrote the Canadian superstar, alongside the announcement on social media. "And of course all of my friends are joining me!!!"

Kicking off May 22 at Rogers Arena in Vancouver, British Columbia, Canada, Lavigne's tour will make stops in cities including Las Vegas, Phoenix, Toronto, Nashville, Chicago and more before wrapping on Sept. 16 at Rogers Place in Edmonton, Alberta, Canada.

Lavigne's latest release was 2022's Love Sux. The 12-track album is produced by Travis Barker's DTA Records and features collabs with Machine Gun Kelly, Mark Hoppus and Blackbear.