The music mogul was attending the press launch of the X Factor musical I Can't Sing! when he was given the adorable gift.
The little white babygro had an image of Simon's beaming face printed on it, which matched the TV personality's own expression as he held it up to the amusement of the audience.
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Simon light-heartedly took in the jokes at the press launch — mostly about love childs and yachts —and even answered one about his notoriously high trouser waistline.
"They are not that high anymore," he said, according to The Guardian. "They used to be."
Speaking on a more serious note, Simon went on to praise the writer of the X Factor musical, Harry Hill, for capturing the real essence of the TV show.
"I didn't want to do a musical that we took too seriously," he said. "The X Factor is a serious show but it's also a fun show and I like Harry's sense of observation.
"The big thing for me were the songs, were the songs going to be good or not. I said if the songs are bad, I'm out. And I stayed."
Simon also spoke of his joy at seeing the baby scan for the first time, saying the experience was "surreal".
"You see this thing which is now alive, moving around," he said. "I am happy."
Lauren is thought to be 12 weeks pregnant with Simon's baby. She reached a divorce settlement with her husband of ten years last month.
Simon — whose fortune is estimated at $368million — was cited as a "co-respondent" in the court papers for adultery.