The Good German

Jacob "Jake" Geismar (George Clooney), an American war correspondent, returns to Berlin during the Potsdam negotiations between the Allied powers after World War II is over in Europe but before hostilities end in Asia. Jacob witnesses his murdered driver, a black-marketeering American soldier named Tully (Tobey Maguire), being fished from a river eddy, suspiciously adjacent to the Potsdam conference grounds. The corpse is discovered to be in possession of 100,000 German reichsmarks which are later revealed to have been printed by the U.S occupying forces.Geismar becomes entwined in both the mystery of his murdered driver and the clandestine search by both Soviet and American forces for the missing German Emil Brandt (Christian Oliver). He becomes more involved in both mysteries as his investigation intersects with his search for Lena Brandt (Cate Blanchett), a German Jew - and Emil's wife - with whom Geismar had been in a relationship prior to the war. Lena has survived the Holocaust by doing "what she had to" to stay alive - early in the film this is assumed to be just prostitution, but Lena, in reality, holds a darker secret of complicity and guilt.In the film, Emil Brandt is a former SS officer who had been the secretary of Franz Bettmann, Chief Production Engineer of the V-2 rocket at concentration camp Mittelbau-Dora/Mittelwerk. (Bettmann is only a minor character in the film; he appears to be based on the real Arthur Rudolph.) The Soviets, the Americans, and the British all try to get hold of Emil Brandt, for different reasons. The Americans have already detained Bettmann in a safehouse and intend to transport him to the U.S. as part of their Operation Overcast/Paperclip to have him work on their own rocket program. In the film, they are fully aware of Bettmann's role at Camp Dora and know about the slave labour used in the V-2 program, but want to cover up his involvement (because they could not lawfully employ a known war criminal), which includes eliminating Emil Brandt, whose testimony or written notes would prevent their whitewashing of Bettmann.Geismar, in his attempts to get his former lover, Lena, out of Berlin, gets more and more involved in the search for Emil Brandt. At one point, Lena gives Emil's notes on Camp Dora to Geismar. When Lena and Geismar try to hand Emil Brandt over to the American prosecutor charged with handling war crimes cases, they are intercepted by the American authorities who want to protect Bettmann, and Brandt is murdered. But Geismar still has Brandt's notebooks, which he now trades in to the war crimes investigators of the U.S. Army (who have turned out to be in league with the other American authorities - the ones who want to keep that evidence confidential to whitewash Bettmann) in exchange for a Persilschein (a denazification document) and a visa for Lena, such that she can leave for England or the U.S. (which one is not made clear in the film).Through a minor character of a Jewish owner of a pawn shop who survived the Holocaust with his legs amputated, the film refers to the Nazi human experimentation, in particular to bone transplantation experiments as they were done at the Ravensbrück concentration camp.

Question: What is Geismar's relationship with Lena?
Answer: Former lover.