Talking about the Jupiter Lagrange points at 60 degrees only. Hard to imagine a scenario where an asteroid comes from outside or inside the orbit of Jupiter and stops at a Lagrange point. That's like tossing a cone on a table and trying to make it end up standing on its nose. Or make the nose flat, it is still very hard. With asteroids it seems impossible without some sort of "brake" applied at the right time. Maybe the influence from a neighbouring planet passing by at the right time or something? How can it happen with a neighbouring planet and how without a neighbouring planet?