I've thought of LA races as having more stuff to learn, regardless of how ageless they are. For example, I can imagine that races with certain powers need to spend a great deal of time learning how to properly use their powers before going on to study magic or how to fight. The more powers they have, the more time they need to train before going on in life.

This would especially be true if their growth was developmental - in other words, they gain powers only after reaching certain stages of growth. Certain racial abilities may not manifest until puberty, for example. In this case, LA represents how long a race needs for fundamental training before going out in the world.

For truly ageless races, I usually see it as dabbling. A dragon may spend centuries just being a dragon, and then finally one day waking up and deciding to become an adventurer. And even as he does, he's just plain more of a "dragon" than anything else, which could be represented by LA.