Tara Hudson, a 26-year-old from Bath, has lived as a woman her whole adult life and undergone lengthy gender affirmation surgery, but is appealing against being held in an all-male prison with abnormally high levels of violence because her passport still says she is a man.
Despite having received hormone treatment and been medically declared a woman by her doctor, Hudson's plea has so far failed to win over judges.
She is serving a 12-week sentence after admitting assault.
The woman's mother, Jackie Brooklyn, said she was "horrified" after finding out where her daughter was being incarcerated.
"When they said they were taking her to [HMP Bristol at] Horfield I was horrified," she told BBC News, commenting: "I don't think she'll cope with it very well. She's lived as a woman for so long. She is a woman."
Brooklyn added: "To be put into an all male prison, it's like me being put into a male prison."
Tara, pictured, will serve a three-month sentence
But a petition started this week claims the young woman "is in extreme danger of abuse, sexual violence, and even death", and calls on magistrates to reconsider their order.
The plea has garnered tens of thousands of backers since launching on Monday, calling on Bath magistrates to "immediately address the dangers Ms Hudson is facing, and amend her sentence that she may spend it in an all-woman’s prison instead".
Farron told Pink News: "The Liberal Democrats will raise this case in Parliament.
"There is a clear need for a policy change in this area. It looks like the Ministry of Justice needs be dragged kicking into the 21st century.
"As I understand it, Tara has lived all her adult life as a female. I worry potential risk of harm to her in a male prison which was deemed to have levels of violence ‘considerably higher than in similar prisons’ by the prisons inspectorate.”