I don't think it's quite the same. She could have been living a double life and not been an assassin. They aren't synonymous. People live double lives where th

I don't think it's quite the same. She could have been living a double life and not been an assassin. They aren't synonymous. People live double lives where they have multiple families, or other things. A double life isn't only reserved for assasins, so the clarification is actually quite important. The author was explaining that he just found out that his girlfriend was living an alternative life in addition to the one he knew. Then he clarifies, what the "double life" was, it was as an assassin.