The Bachelor alums welcomed their twins - a son and a daughter - over the weekend, Arie announced on Instagram Saturday.
Lauren shared on Wednesday that while their son was able to go home with them, their baby girl had to stay in the hospital. Arie said in a post Wednesday that she "needed oxygen but is doing much better now."
The duo shared a video to their YouTube channel on Wednesday, documenting their 2-year-old, Alessi, meeting her little brother for the first time - as well as the little boy's name: Lux.
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"What's his name?" Arie asked Alessi in the video as the toddler held her little brother. "Baby Lux!"
Lauren previously told PEOPLE that she and Arie picked out their twins' names after choosing Alessi's moniker.
Arie Luyendyk Jr., Lauren Burnham
"We've had them picked out for the last couple of years," she said. "We came up with [our daughter] Alessi's name. Right after we decided on her name, we actually chose the next two for our boy and our girl."
"It just ended up working out where we're now having a boy and a girl. So we're just gonna use both of those names that we loved," she added.
youtube Arie Luyendyk Jr. and Lauren Burnham's twins
Elsewhere in Wednesday's video, Lauren was shown getting emotional as she said goodbye to her daughter.
"It's kind of day to day, to be honest," Arie said in the video of his daughter's condition. "They don't really know if she'll come home tomorrow or the next day, or if she needs even more time.
Arie said that while she is "perfectly healthy," she's "having some trouble with her breathing" and is on oxygen.