There have been several movies made, dating as far back as 1918. The one I found was the 1955 French epic Lola Montès , starring Martine Carol as Lola and Peter Ustinov as the narrator and ringmaster of the circus she ends up working in. It's almost all in French, with a few lines in English here and there. Good English subtitles.
The movie is disappointing from almost every angle. Poor camera work, mediocre acting, downright miserable script, historically inaccurate except in the most general facts. There are, however, some fine costumes, and every now and then excellent make-up work. The sets for the Bavarian royal palace have their moments as well.
Lola's life is fairly well documented, being the daughter of a British Army officer and living a very high-profile adult life. Discretion was not one of her talents. So a few historical/movie comparisons :
Movie: Lola was born in England, her father was a colonel in the British Army in India, where he was killed in battle.
History: Elizabeth Rosanna Gilbert was born in Ireland, her father was in the British Army. He was dispatched to India and his family joined him there, where he soon died of cholera.
Movie: After her father's death, her mother "keeps" the colonel's adjutant, whom Lola seduces and marries.
History: After her father's death, her mother marries another officer, and sends Lola back to Scotland to live with his parents. Lola, at 16, elopes with a Lieutenant James and finds herself back in India with him. She escapes back to London and becomes an exotic dancer under the stage name Lola Montez.
Movie: Lola uses her charms to become member of the ballet troupe in London where she makes her dancing debut
History: Lola performs her own invention, the tarantula dance, at a London theater, but the show is interrupted when many people recognize her as the wife of the well-connected Lt. James. She returns to India for a divorce, then back to Europe to launch a career as a courtesan.
Movie: Lola ends up as the center attraction of a circus act
History: Lola has a stroke at age 39, and dies of pneumonia in NYC just before her 40th birthday.
The movie ignores her move to California (where she got married to a shop keeper and tried to settle down), and her 5 years entertaining miners in Australia's gold rush.
Sadly, of all the movies listed in imdb.com for Lola, this is the only "talkie" which comes close to being a full biography. I think Hollywood is missing out here.