Avid Lost Fan from London, real name's "Tim".
Well the obvious theme that Karamazov has in common with Lost is patricide. Ben, Kate, and Locke (indirectly) all kill their fathers, just as Ivan, Alexei, Dmitry and Smerdyakov all in various ways bring about their father's death. It's a little more subtle in Karamazov, but we can expect that from a book, or Dostoyevsky in particular. Again, like Lost, the father is by no means an innocent victim, Fyodor Pavlovich is brash, selfish, irresponsible and immature, and it is no surprise that the sons dislike him.
The other major point that comes to my mind is duality. Lost has various themes of opposition: black and white, fate and free will, faith and reason. The Karamazov Brothers also treats faith and reason through Alexei and Ivan respectively, but in my opinion it ultimately sides with faith as Ivan undergoes his mental downfall after his visit from the "devil".
The tension in Karamazov is certainly evident, though it is a different kind of tension to that of Lost, not least because of the different medium. Dostoyevsky is very good at keeping tension within one fixed scene and conversation, like Dmitri's questioning, or his trial, whilst Lost will often compare multiple scenes and call into question previous assumptions. But ultimately both make you crave the answer, and require a lot of commitment to get it (1000+ pages of book or 100+ hours of television). But I think they're worth it.
Recently I suggested distinguishing shared centrics from individual centrics in character infoboxes. Someone requested to see an example, so here's a few examples of the major characters and how it will work. The extent of centricity is, of course, debatable, but I think most of the distinctions I make here side with the majority.
WORK IN PROGRESS