Just started watching the Disappeared series for the first time, and saw the LC episode. Very tragic. However, I don't see this being as much of a mystery as they're making it out to be in the episode.
I have read the "Into the Wild" non-fiction book about the young man (Chris McCandless) wanting to live away from society. CM ultimately died in the somewhat remote wilderness of Alaska after eating a poisonous plant - probably unintentionally, by all accounts.
Since LC was a fan of the book & also appeared to be suffering from depression, it seems evident that he was emulating what happened in the book to some extent by leaving his family & moving out to the woods in a somewhat remote area (but not that remote), etc.
As far as what happened to him, I strongly suspect he probably passed in the general area where his clothes/belongings were found. As to why his body hasn't been found, it's very possible he went into the near-by river, drowned, and was swept away by the current. If that were the case, he wouldn't have necessarily been found in that specific area.
An other possibility is that he passed in the woods, and was then dragged off by animals, etc. - that could also explain why he wasn't found.
Lastly, even though there was an extensive search of the area - IMHO it's also possible he was missed.
I don't believe he went overseas to "start a new life" - as was suggested by the episode. If that were the case, he would have needed money, a passport, etc. Also. he would have had to buy a plane ticket & there would be some kind of "trail" at airports & other places, etc. And, if he were still alive I don't think he would have left for this long without at least contacting his family at some point - which obviously never happened.