Lilja has played the piano since the age of 7. Since 2007, Lilja has been studying with Peter Mate at the Reykjavik College of Music.
At the age of 10 Lilja played with the Icelandic Symphony Orchestra as a soloist. She was a finalist in the EPTA piano competition in Belgium 2008 and winner of the EPTA piano competition in Iceland 2009 and 2012.
In 2010, Lilja won the special interpretation prize for the Chopin Competition organized by the Polish Embassy in Reykjavik to celebrate the bicentenary of the composer's birth. In February 2015 Lilja played the Shostakovich piano concerto no. 2 with the Reykjavik College Symphony Orchestra.
In July 2015, Lilja was chosen to represent Iceland at the Tianjin international arts and culture festival in China. Lilja is currently at the CRR de Paris in the class of Billy Eidi.