Leave the Graphic Novel Behind
By now, fans know the basic story of Watchmen: the 1985 murder of Edward Blake, revealed to be the costumed government operative called the Comedian, triggers an investigation by the masked vigilante known as Rorschach. As Rorschach follows the clues surrounding Blake's murder, he discovers a complex conspiracy surrounding his fellow superheroes, who have all been forced to retire by government mandate. The story then explores the decades-long history of masked adventurers and the dawn of Doctor Manhattan, the first and only superpowered being in this universe, and how their existence altered and upended the world order. Eventually, the trail leads to the discovery of a master plan by Adrian Veidt, formerly the hero known as Ozymandias, to stage an attack on New York City in order to force the governments of the world to pull back from the brink of nuclear Armageddon. At least in a nutshell.
In spite of whatever grievances fans have with Snyder's Watchmen, his film told the story of the graphic novel very well. Lindelof's Watchmen series may be expected to adapt this same story beat-for-beat, but seeing Watchmen's story told again, just a decade removed from the film's theatrical run, would inevitably feel redundant, even if Lindelof's series manages to improve upon aspects of Snyder's work. The investigation by Rorschach that Snyder's film focuses on is just one thread of many complicated themes and explorations of characters and deconstruction of the tropes of comic book superheroes Watchmen is really about.
A lot of the meat on Watchmen's bones is found in the various ancillary material provided by Moore and Gibbons. Each chapter of the graphic novel was book-ended by extras that enriched the Watchmen universe: Pages of Hollis Mason's autobiography "Under the Hood," excepts from interviews conducted with Adrian Veidt, and of course, the pirate graphic novel "Tales of the Black Freighter," which was woven through the text of the graphic novel. Lindelof would have the leeway on HBO to really delve into that material. Departing from the "modern day" of 1985 in the story (or even setting Watchmen in our modern day) and spending ample time exploring the history of the Watchmen universe is something only an HBO series could best accomplish.
Similar to how AMC's Preacher and The Walking Dead unshackled themselves from their source material as they saw fit (as did Game of Thrones in diverging from George R.R. Martin's novels), Lindelof would be best served by letting the 2009 movie be the "slavish" adaptation and using his series to do the unexpected with Watchmen.