Lost is clearly sci-fi, and therefore on-topic here, on this site.
Lost is a television show, and therefore on-topic for movies.se.
When you go to ask a question that fits on either site (and there are tons of questions here that would be appropriate for either site, and a fair number on movies.se), pick which site you think is more appropriate.
That's it. It isn't any more complicated than that, aside from the caveat: don't cross-post your question on both sites.
If your question is about the background of the actors, about the process of filming the show, the production, the non-fictional settings, or any other element that could be applicable to most television shows that aren't science fiction, then you might get better results on movies.se.
If your question is about the fantastic elements (such as Why, and how, was the island protected?), then it may be better here, since we specialize in science fiction and fantasy discussion.
In most cases, you really can't pick the "wrong" site. In the few cases where it is clearly more appropriate for the "other" site, the community will discuss it, and it likely will be migrated.
So getting back to your original suggestion of migrating everything with the lost tag to movies.se: Absolutely not.
If we migrate it because it's a TV show, then we might as well migrate every other question on TV shows or movies we have here, which would essentially shut our site down.
If we migrate it because it's a TV show, and the scifi elements occur more as a background upon which non-scifi elements frequently form major plots, we'd still wind up with a policy that declares a tremendous amount of our content off-topic here, for essentially no reason other than an arbitrary line drawn in the sand.
For reference, here is the original community discussion on how we handle "conflicts" with movies.se and (the now defunct) literature.se.