Contrary to popular belief, Lost season 2 killing off Ana Lucia and Libby so suddenly was not due to the DUI arrests of actors Michelle Rodriguez and Cynthia Watros. Ana Lucia Cortez and Elizabeth "Libby" Smith were introduced into the story proper early in Lost season 2, as two survivors from the tail section of Oceanic Airline Flight 815. Their survival had been unknown to Jack, Kate, Sawyer, and the rest of the main group, who crashed on a different part of the island.
Ana Lucia quickly asserted herself as the leader of the tail section survivors, but also quickly drew ire from audiences for her overly combative and antagonistic behavior toward the main characters. Her accidental murder of Shannon, who had herself been partially redeemed due to her love affair with fan-favorite Sayid, furthered the backlash against Ana Lucia. By contrast, Libby developed a rather charming relationship with Hurley, which saw the two growing closer romantically prior to Libby's sudden demise by gunshot.
Said gunshot deaths for Ana Lucia and Libby came in the Lost season 2 episode "Two for the Road," as they were shot by the normally friendly Michael, who had been coerced by The Others. This episode aired mere weeks after Rodriguez and Watros were both arrested for driving under the influence of alcohol, so the common wisdom quickly became that they had been kicked off the show due to those charges. In actuality, Ana Lucia's death had been planned from the beginning, as Rodriguez didn't want to do more than one season. The decision to kill the mysterious Libby as well was due to Ana Lucia's unpopularity, as producers thought Libby's death would be a more shocking and emotional moment.
While it's logically quite understandable why so many ended up attributing the deaths of Lost's Ana Lucia and Libby to their actors' real-life misbehavior, and even understandable why that belief has remained widely held even today, anyone with a knowledge of how Lost was made would really know it wasn't true. Lost was one of the first of many big-budget prestige dramas made for network TV in the 2000s, and its episodes were written and filmed well in advance of their actual airing. The decision to kill off Ana Lucia and Libby was made long before any arrests occurred, and the timing was entirely coincidental.
As mentioned above, Fast and Furious star Michelle Rodriguez made it a condition of signing on that she would only star in one season of Lost. In regard to Libby, Lost's writing and producing staff actually planned to bring her back for following seasons and reveal more about her mysterious past in flashbacks. Unfortunately, Cynthia Watros ended up too busy with other projects to make more than a few brief appearances in subsequent seasons, although she did get to reunite with Hurley in Lost season 6's afterlife. As tempting as it is to attribute Ana Lucia and Libby's shocking and sudden demises to scandal, the reality is much more mundane.