When you tell her it's time to go after him, she'll leave her office to go to her apartment. But for the second time around, when you started a new game without an imported character, going through Genesis was necessary for you to fill in (and, the game presumes, for you to learn) Shepard's back-story up to that point.Once you're given the option to visit Ilium, you can stop by Liara's office and give her some information from Cerberus regarding the location of the Shadow Broker. The fact that you had a save game to import implies that you've played Mass Effect (1), and thereby know the history, and the import itself handles configuration of all the critical decision points from the first game. If you imported a save game from Mass Effect, the first time you played Mass Effect 2, then there would have been no need to run Genesis. The Mass Effect series, as I'm sure you recognize, is very story-heavy and player decisions play an extremely important part throughout the whole trilogy. This was a good thing to have at the time for players who chose to migrate from the Xbox for the series' second installment, and was absolutely essential for PS3-only players. The purpose of this interactive introduction to Mass Effect 2 is to fill in some of the story a player might have missed from the original Mass Effect, and allow them to make critical decisions that would have been made during the first game and will have an effect on the world in the second. This is a free DLC for PS3 players, since the original Mass Effect was not available on that platform when Mass Effect 2 was initially released. I believe the 'comic book story' you're referring to is Mass Effect: Genesis. Addendom to answer, to address the 'comic book story' issue:

Download lair of the shadow broker