Ursa was born in 2023 and her life has been marked by neglect and illegality, the sanctuary said.
She was handed over to the Wild Animal Rescue Centre in Kyiv after being discovered at a private home by police.
Vets found she had a severe intestinal infection, parasites and was significantly smaller than other lynx of her age due to poor nutrition and incorrect feeding.
This means she would never survive in the wild, the sanctuary said.
Cam Whitnall, managing director of the Big Cat Sanctuary, said: “Our mission to rescue the five lions from Ukraine showed the world what is possible when people come together.
“Now, we are asking for that same incredible support for Ursa. She has had a difficult start to life, stunted by poor care and living under the constant shadow of war.
“Ursa deserves a future where she is safe, and we are determined to bring her to the sanctuary, giving her the peaceful, forever home she deserves.”