Lane, a British film producer, made the announcement on social media on Sunday.
"#IncomingPackage best present," she captioned an Instagram pic showing her burgeoning baby bump. "#ThankYouLord #SantaBelly."
In the photo, Lane does a side-by-side split, comparing bellies with Santa Claus.
After breaking the baby news, Lane went on to post two more photos of herself in maternity dresses.
"My official pregnancy dress," she wrote. "I have worn this 1-2x a week every week for past 5 months. It was 3 euros in a charity shop in Ireland. I love #recycled clothes."
She also showed off her "other official prego wego dress," which she bought in Amsterdam for 15 euros.
"Every other day I dunno as I have other dresses but Baby likes these ones ... is super conscious, connected & aware," she wrote. "Has not let me eat much meat entire pregnancy either ... has me thinking about things I'd rather live in ignorance to."
On Monday, Lane posted a sweet note to her fiancé.
"Thank you for the opportunity to be a Mummy, Sweetheart! #ILoveYou #ManCrushMonday #MCM every day for me," she captioned a black-and-white photo taken by a Vikings set photographer. "I was 6 months and barely showing but thought I was m-a-s-s-i-v-e. I will share later as you may fall over laughing am sticking out a non-belly not knowing what was in store for me in just a couple months #firsttimemom #firsttimepregnant #everydayanadventure when you're #largeandincharge."
Lane and Meyers have reportedly been engaged since 2014.
In 2007, Meyers told People he was looking forward to fatherhood after watching fellow actors Tom Cruise and Will Smith interact with their children.
"I'm very broody, but I'm not ready to be a father," he reportedly said at the time. "I do love children, though. When I was on the set of Mission: Impossible 3, Will Smith and his wife came down, and he's got a little girl and a little boy. They were so beautiful and it was lovely to see that family unit. It's the same with Tom. He has a great family unit."