The duo shared a cozy lunch, followed by a stroll through Central Park Saturday

By Kathy Ehrich Dowd
April 06, 2015 10:30 AM
Christopher Polk/Getty; Barry King/FilmMagic

With spring finally in the air, under-the-radar couple Jennifer Lawrence and Chris Martin enjoyed a cozy weekend in New York City in a famously romantic spot: Central Park.

On Saturday, the duo were spotted enjoying lunch at Tavern on the Green, located inside the park, where they tried – unsuccessfully – to keep a low profile.

“They were very nice to everyone,” a source tells PEOPLE, adding that Lawrence, 24, enjoyed a roast beef sandwich while Martin, 38, munched on eggs Benedict. “Because their table was facing the courtyard and was against the glass wall, people pretended to be taking selfies so they could be seen in the background. It was very funny.”

“They were at their seats for all of 45 minutes before leaving and strolling through Central Park,” the source added.

The duo walked through Strawberry Fields, a living memorial to late Beatle John Lennon, according to Page Six. A second source tells PEOPLE the duo returned to the restaurant following their stroll, hopped into a waiting car and went to the Carlyle Hotel, where they spent the night.

Around 2 p.m. the next day – Easter Sunday – the couple headed to Teterboro Airport in New Jersey and seemingly boarded separate flights.

The weekend marked the first time the couple were seen in public since they attended Harry Styles’ 21st birthday party in Los Angeles on Jan. 31.

Their low-key Easter weekend was seemingly in sync with their low-key approach to their relationship, as the Oscar-winner juggles filming Joy in Boston while Martin helped pal Jay Z launch a new music-streaming service, Tidal, last week.

“They see each other when they can, yet each continues to do their own thing,” a Martin source recently said. “Both have full plates, and they like it that way.”

Martin has also stayed notably friendly with ex Gwyneth Paltrow, 42, who was spotted having a little Easter weekend fun of her own Sunday night. The Oscar winner was seen dining at Chinois on Main in Los Angeles with Brad Falchuck, the Glee and American Horror Story producer she’s been linked to for more than a year.

With reporting by SONAL DUTT, MARY GREEN and BLAINE ZUCKERMAN

VIDEO: Jennifer Lawrence and Chris Martin Spotted in Public for the First Time in Months

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