After meeting with the lawyer on Wednesday, President Dalia Grybauskaitė signed a decree in support of the government's bid to propose the candidate to the EU General Court, the presidential press service said.
The Lithuanian candidate judge must be proposed by the government following approval from the president and consultations with the parliament.
The EU General Court consists of at least one judge delegated by every of EU's 27 member-states appointed for a six-year tenure.
The term of Lithuania's current delegate Vilėnas Vadapalas is scheduled to expire on 31 August 2013. Dambrauskaitė is proposed to replace him.
The General Court hears disputes of private individuals, companies, and some organizations, as well as analyzes competition law cases.
Dambrauskaitė is currently a professor at Civil and Commercial Law Faculty of the Law Department at Mykolas Romeris University. The candidate has a doctoral degree in law she acquired after defending thesis in the Lithuanian and French languages at universities in Lithuania and France.