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"Senna james + lux jacob," she wrote.
Lauren also wished Arie a Happy Father's Day on Instagram by writing on her Instagram Story -- which Arie later reposted -- "Happy father's day to you my love. Thank you for being an even more incredible daddy to our babies than I ever could've imagined."
Arie and Lauren were thrilled to welcome their baby twins via C-section on June 11, but Lauren said several days later it was "so bittersweet" to leave the hospital with Lux considering Senna had to stay behind.
Lauren uploaded a video on Instagram in which she was rubbing her baby girl's hand, and she wrote, "I've never felt heartbreak like this. Pls say prayers for our girl."
Senna apparently "needed oxygen" and "a little support" four days after her birth while Lux only spent "a few hours" in the NICU after his arrival.
Arie and Lauren are also parents of a two-year-old daughter, Alessi, who was born in May 2019.
Now that the whole family is together, Arie hasn't refrained from posting adorable photos of Alessi holding her infant siblings on Instagram Stories. Alessi is also apparently practicing how to be a good big sister with her dolls.
Arie shared the first photos of the newborns with their mom on Monday, June 14, when he gushed about Lauren.
"Never been prouder of my wife than in this moment," Arie wrote on Instagram. "She is the strongest woman I know and I'm lucky to be on this incredible journey with her. We are proud parents of a healthy boy and girl!"
Arie surprised Lauren with a backyard baby shower for their twins in late April when Lauren was 29 weeks along in her pregnancy.
As for where they plan to live with their three children, Arie and Lauren recently bought a house in Hawaii, although they won't stay there "full-time." The pair reportedly plan to split their time between Hawaii and Arizona, according to Us Weekly.
Lauren finished Arie's season of The Bachelor in second place when Arie actually chose Becca Kufrin as his winner and popped the question to her during the Final Rose Ceremony, which aired in March 2018.
But weeks after getting engaged, Arie decided to dump Becca because he claimed he was still in love with Lauren, and so he begged Lauren for a second chance.