Summer before 7th year, Harry runs away from the Dursleys and is hiding at Grimmauld and venturing into the Muggle world to keep sane since Grimmauld isn't that inviting. Ron and Hermione intend to join him after the wedding.
During one of the trips, he goes to the Natural History Museum, where he walks into a young woman who is doing a summer internship there. It's a slow day, they start chatting about the exhibition and her studies and hours pass. Lara asks Harry out for a coffee after her shift. Sure enough, they go out and have a pleasant evening, Harry forgetting about the looming war and entertaining her with Muggle-friendly versions of his Hogwarts adventures. They agree to meet again the next day ("It's a date"), Harry visits for her lunch break and brings her a rose, which she finds cute. However, a few Death Eaters decide to ruin the mood and attack the pub they were at (random attack, they did not expect Harry). Harry manages to take them by surprise, although one calls for reinforcements via Dark Mark, so Harry decides to retreat, apparating away with Lara side-along. Which leads to an awkward "I guess you have some questions" discussion in which Harry tells her about magic. He also lets some things about the Horcruxes slip, so that it sounds like an exercise in archeology to Lara (he doesn't say much, but tracking down magical items and a bit of imagination should do the trick). Lara then wants in on the hunt.