Hall, a former model and fashion designer, had started working as an artist when he died.
He is survived by his eight-year-old daughter, River, with former Real Housewives of Cheshire star Missé Beqiri.
In her post, Lewis wrote how being a father was “the most important thing” to Hall and praised him for making parenthood “look so easy and effortless”.
She also reflected on how the weeks since his death have “felt very surreal”.
“You were such a massive and special part of my life, and I truly hoped that we would grow old, that I’d see you one day, happy and at peace with life,” she wrote.
Lewis added: “I’m sorry I couldn’t have saved you.”