In India, we say, "It was a one legged hen."
"This saying may have originated from an incident where a king's cook ate a chicken leg while preparing biryani. When the king asked about the missing leg, the cook claimed it was a one-legged hen. Despite being caught, the cook stubbornly stuck to his story, leading to the phrase 'one-legged hen' describing someone who stubbornly clings to a false claim."
I am looking for an English equivalent which can be used to describe someone who is being stubborn or sticking to their own false or incorrect statement.