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Lizzo just scored a win in her legal battle against 3 former backup dancers ... the women have dropped their claims that Lizzo fat-shamed them, despite the rest of the case moving forward ... TMZ has learned.

Lizzo's powerhouse attorney, Marty Singer , and his partner, Melissa Y. Glass , tell TMZ the fat-shaming claims were a major part of the sexual harassment lawsuit brought by Arianna Davis , Noelle Rodriguez , and Crystal Williams , but they insist it always lacked merit.

According to Lizzo's attorneys, the allegations were refuted by 18 witnesses in sworn declarations submitted to the court.

They say the Superior Court judge concluded Davis was fired because she made "an unauthorized recording of Lizzo in a dancer meeting and sent it to Williams, who was no lon

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