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Lola Young collapsed during her set at a music festival in New York City ... one day after canceling a different concert "due to a sensitive matter."

The British singer was performing her hit "Conceited" at the All Things Go Music Festival Saturday evening when the incident went down. Social media video shows her giving the powerhouse vocals she's known for ... when she abruptly stops to say a few words to her keyboardist, seemingly asking for some water. TikTok/@6davidhatezyou9

She stumbles back ... and then passes out on her back. Her keyboardist and other members of her team rushed over to her and carry her off the stage.

Lola later hopped on Instagram to let fans knows she was "doing okay" and thanked them for their support.

Earlier in the set, she had let concertgoers

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