Fan Theory: Landa thought Shosanna was recruited by the Basterds.
Landa definitely knew it was Shosanna, but truthfully didn’t care. He has nothing to gain from killing Jews at this point in the war. The Germans were losing the war, and he’d almost certainly be tried as a war criminal. He also knows that the Basterds are willing to recruit along the way. They recruited Stiglitz, Hicox, and von Hammersmark. As head of security for the event, he definitely would’ve notice the massive pile of flammable film behind the screen. He could’ve theorized that the Basterds made contact with her and offered her revenge on the Nazis, if she was willing to destroy her movie theater. He could’ve also made the assumption that burning down the theater with nitrate was a back up plan in case their explosives failed. Either way the theater was destroyed and the German High Command was dead. By the time everything and everyone was up in flames, Landa cut a deal with the United States.