Lady Gaga is enjoying a little less applause and a lot more lullabies these days.

The pop superstar and her fiancé, Michael Polansky, have been settling into life with their daughter, Rose, while doing everything they can to give her as normal a childhood as possible, a source exclusively told Page Six.

“Gaga and Michael have really been enjoying their little family bubble,” the insider said. “They’ve started taking Rose on little outings together, but for the most part, they’re keeping things very private.”

The “Born This Way” singer, 40, is “fiercely protective of her daughter and very particular about who she allows into their inner circle…

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