The performer died over the weekend, their publicist Simon Jones announced on social media.
He described Williams as “an incredibly loved, warm-hearted and amazing person”.
On Facebook the theatre shared their tribute to the performing star.
It read: “We are beyond devastated to hear of the passing of James Lee Williams, The Vivienne.
“Not only were they a formidable drag queen but also an immensely talented musical theatre performer who created and delivered the most inspired Wicked Witch of the West in The Wizard of Oz here last summer.
“A role they played to critical acclaim and an outpouring of love and support from our audiences.
“Our thoughts are with their family, friends and the Wizard of Oz company.”