The 37-year-old reached an amicable divorce settlement with her ex-husband in August, one month after the news broke that she was expecting a baby with Simon.
Both Lauren and Andrew have agreed to share joint custody of their seven-year-old son. It has also been reported that the settlement includes a $2million payment to Lauren.
In August, the US socialite said in a statement, "I am committed to sorting things out with Andrew as amicably as possible to ensure the well-being of our son. I would hope for some space and privacy in order to work through this."
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Lauren and Simon are expecting a little boy together early next year. It is thought she will give birth in New York, to be close to her mother Carole Sandford.
X Factor mogul Simon has already revealed his top two name choices for their son — Simon because "I like the name", and Eric, after his late father.
With Christmas and the arrival of their first baby together just around the corner, Lauren and Simon have a lot to celebrate. And they might also be toasting their engagement over the festive period, with numerous reports stating that Simon plans to propose.
The TV star is said to have bought an engagement ring, and is preparing to pop the question.
"Simon has an engagement ring but is being secretive about the proposal," a source told People. "Simon is flying to the Caribbean for the Christmas holiday. Lauren will join him for parts of the holiday trip.
"Simon could be planning a special holiday proposal. It seems he will definitely propose."
Meanwhile, Lauren's baby shower is set to take place this weekend. According to E!, the intimate gathering will take place at a private residence in LA, with just close friends and family in attendance.