What do you want from a sequel?
Loved this game even though it was somewhat monotonous. The setting and production design were fantastic, the gameplay was innovative and immersive (though kind of monotonous, as mentioned), and the story, dialogue and voice acting were all impeccable and created a spellbinding tone and atmosphere, second to none. And the score, so goddamn good. But the game was lacking in certain areas.
First of all they need to let us explore the world more. LAN was way too linear. I think the game would have benefited greatly from a layout closer to GTA, an open world where you have several mission locations, one could be the precinct he's working at at the time, and then add some characters he's working with on the side. Making the main character a corrupt cop who takes his job seriously but get's into some questionable extracurricular activities would be cool. That way you could add add all perks that entails, like in the GTA series. Or just take the Red Dead approach. Good guy who can do bad stuff. Making him a P.I. would actually be perfect, that way he isn't bogged down by the whole being a good cop thing. Basically more freedom is what I want. More side quests.
Hmm what else? That would be a good start, if LAN had these elements it would have been absolutely fantastic.