Born in Bucharest, Lara is the only child of Valentin Plătăreanu, an actor, and his wife, Doina. In 1983, her family decided to flee to West Germany to escape Nicolae Ceauşescu's regime in Communist Romania. Although the family had originally planned to emigrate to Canada, they settled down in Freiburg im Breisgau, Baden-Württemberg, before eventually moving to Berlin.

After graduating at the Französisches Gymnasium Berlin in 1997, Lara went on to study acting under the management of her father, co-founder of the Theaterwerkstatt Charlottenburg, finishing in 2000.

By sixteen, she was playing lead roles in various television dramas; since then, she has appeared in films, including as Traudl Junge, Adolf Hitler's secretary, in the Academy Award-nominated 2004 film Downfall; following this, Francis Ford Coppola wrote her a letter and gave her a leading role in Youth Without Youth (2007).

In 2007 she also appeared as Belgian Journalist Annik Honoré in the film Control, the Ian Curtis biopic. In 2008, she served as a member of the Cannes Film Festival jury. She played a lead role in Greek Director Theo Angelopoulos's 2008 film The Dust of Time, opposite Irène Jacob and Bruno Ganz. She has also appeared in several French productions, including Napoléon and L'Affaire Farewell. She appeared in The Reader and Der Baader Meinhof Komplex which were both nominated for the 81st Academy Awards, for best picture and best foreign language film, respectively.

In August 2009, Lara married English actor Sam Riley, with whom she acted in the films Control and Suite Française. In January 2014, she gave birth to their first child, a boy.