At the age of six Astanova entered the V. Uspensky Specialized School of Music for Gifted Children, an elite school in Tashkent, present-day Uzbekistan where she was born, grew up, and where she started studying piano under Professor Tamara Popovich. She frequently visited Moscow, studying at the Tchaikovsky Moscow State Conservatory for lessons with Professor Lev Naumov, who described Astanova's pianism as "rare and truly ingenious", adding that "Chopin performed by Lola is simply outstanding."
Astanova started touring as a concert pianist at the age of eight. She performed in Germany, France, Austria, Italy and Russia in both solo programs and performances with orchestras. She became a laureate at the 1996 International Chopin Competition for Young Pianists in Moscow. In 1998, she was featured in the UNESCO documentary "Prodigies of the 20th Century". In 2003, she emigrated to the United States. Astanova had her US debut in 2004 at the John F. Kennedy Center for the Performing Arts in Washington, DC.
Astanova became a star of the October 2007 Classical Superstars Fantasy Concert alongside Valery Gergiev and Kirov Orchestra of the Mariinsky Theater, hosted by ABC's television host Regis Philbin. The concert was featured in the 100th anniversary issue of the Neiman Marcus Christmas Book and offered for $1.6 million. In August 2008, The National September 11 Memorial & Museum announced Ms. Astanova's performance on the famed Steinway concert grand piano of Vladimir Horowitz at the "Notes of Hope" benefit hosted by Mayor Michael Bloomberg. The event included performances by comedian & actor Denis Leary and rock musician John Mellencamp.
On January 19, 2012 Astanova made her Carnegie Hall debut. A special Tribute to Vladimir Horowitz gala concert was chaired by Donald Trump and hosted by the Academy Award Winner Julie Andrews. Horowitz's student, American pianist Byron Janis was among the concert's attendees. All proceeds from the performance were donated to the American Cancer Society. In March 2012, Astanova appeared on the cover of Palm Beach Society magazine ahead of her performance with Jahja Ling at the Kravis Center. On May 30, 2012 she performed a duet with Byron Janis during his Lifetime Achievement Award ceremony at the Lincoln Center for the Performing Arts.
Astanova teamed up with Jahja Ling several more times, performing with the San Diego Symphony in 2012 and 2014, with the Orchestra of St. Luke's at the Lincoln Center for the Performing Arts in New York City in 2013, and with the Cleveland Orchestra at the Mar-a-Lago in Palm Beach in 2014 Among Astanova's long-running symphonic collaborations were also performances with Eduardo Marturet and the Miami Symphony Orchestra, Ramón Tebar and the Palm Beach Symphony and Gerard Schwarz and the All-Star Orchestra
Astanova's performance of Gershwin's "Rhapsody in Blue" with Gerard Schwarz and the All-Star Orchestra, featured in the "All-Star Orchestra "Visions of New York" television special, received the 2016 Emmy Award.
Astanova has received attention for her performance style and appearance, often wearing high-heels and sporting exclusive haute couture outfits. She has expressed her love for fashion stating that "some extraordinary artists" work in this field. In June 2012, she was named among Top 10 Style Icons in Classical Music by Limelight magazine.
In 2014 Astanova performed at the New York Ball honoring editor-in-chief of Vogue Italia Franca Sozzani, with Donald Trump, Valentino Garavani, Baz Luhrmann, Steven Klein, Zac Posen, Coco Rocha, and Peter Dundas attending the event and Kris Jenner introducing Astanova on stage.
Astanova has been featured in numerous style and lifestyle publications, including Vogue, People, ¡Hola!, Haute Living and Quest.
Astanova has written a number of virtuoso piano transcriptions on the theme of popular melodies including holiday classic "Jingle Bells" and Rihanna's "Don't Stop the Music".
In 2016 Astanova performed her arrangement of Liszt's La Campanella as a duet with electric guitar.