LOST AND FOUND

It may be as simple as a child's concept of lost and found.  When a child loses something they want, they cry to their parent to find it. Or replace it. Or find it again. In a material world, people do hold onto certain things tightly for personal or sentimental value, like a child's first teddy bear or blanket.

There is something comforting that strangers in public places have lost and founds, where people who have lost something may have an opportunity to regain what they had lost.

The same can be applied to LOST.

The main characters "lost" something they needed to find.

Example, Jack lost his father and he was desperate to find him.  In the process of the search, Jack himself lost his own mind to alcohol and drugs. The ironic twist to his search was that images of his ghostly father were smoke monster illusions, and that in order to find his father Jack had to die.

Hurley could have had a similar path. He lost his father by abandonment at an early age. But Hurley did not go searching for his father. His father returned to the family only after Hurley won his cursed lottery winnings. With sudden wealth, Hurley lost part of his innocence and his ability to be his simple self. People wanted things from him (his money). He became more reclusive and sad. His lost his simple life, so he went to find the answer to the cursed Numbers. He found them throughout the island - - - as premonitions of danger and pain. In another ironic twist, Hurley found the life he was looking for with Libby only after he died.

Sawyer lost his family at an early age. He vowed to "find" the man responsible for ruining his life. In another ironic twist, Sawyer's search turned him into the con-man he resented for his entire life. It led him to killing an innocent man. He was no better than Cooper. It was after he crashed on the island did Sawyer find the man who ruined his life, and took his revenge. But that did not solve the problem that he lost his life in the process of revenge. Again, he only found true happiness without deceit or deception after he died in the sideways world with Juliet.

The island could be symbolic as a lost and found box. In it, various aspects of a person's life that had been discarded or lost could be found.

But what did the characters actually find on the island?

Friendship?
A purpose?
Romance or love interest?
Self-esteem?
Moral guidance?
Death?

It seems those factors only came to light in the sideways world.