Lund has worked as a film critic for NATT&DAG (Norwegian; translation, Night&Day), and as a journalist, after earlier work as a fashion model. She has been working as an actor since 2011, appearing first as the character Diana Brown in Morten Tyldum's BAFTA Award film Headhunters (Norwegian, Hodejegerne), an action thriller based on the 2008 Jo Nesbø novel of the same name. The BAFTA Award nomination was for Best Foreign Language Film. Lund's entry into acting is described, thus, by Headhunters co-star Aksel Hennie: "When I first read the script I pictured Synnove because I knew her from before and she had reviewed every single film I've done and Morten (the director) asked me, 'Is she a film critic? Yeah. Has she review any of my films? Yeah. Was the review good? Yeah. OK then we can try her', So we tried her and she came so prepared — more prepared than any actress."