Considering how much we've seen him stress about it ("What do you want me to DOOO?!") I'm betting it's the first: he stopped looking and gave up - maybe when he was told he couldn't do the Outback thing - and then found It by accident, literally. He seems to feel that he's very much a part of Its Plan, that his actions are important to The Plan, so I don't buy that he believes things will work out by themselves and he can just relax. But he does seem very relaxed, as long as he believes he knows what his part of The Plan is. Knowing what The Plan is, doesn't seem as important to him as the belief that there is one.
I don't like John Locke at all. I think he's crazy, and dangerously so, not crazy in the entertaining rub-soup-in-his-hair way.
edited for clarity; imagine what it was like before