Luján earned the Woman Grandmaster (WGM) title in May 2005 for her results at the 35th Chess Olympiad in Bled 2002, the American Continental Chess Championship in Buenos Aires 2003, and Ciudad de Chacabuco tournament in Buenos Aires 2004. She earned the open International Master (IM) title in January 2007, for her results at the American Continental Chess Championship 2003, Vila de Sort 2006, and Ciutat de Balaguer 2006.