Seems to me that in terms of describing behavior (as opposed to universal forces or ethical ideals), law and chaos relate to your interdependence with other creatures, places and things.
A lawful creature is like one cog in a machine, regardless of whether it's a good machine or an evil machine, a fishing machine, a military machine or any number of other systems. It expects neighboring cogs to be positioned and turned appropriately, and its neighbors can rely on it to be that also. The machine only functions efficiently when every piece is in the right place and doing the right thing. Keeping the machine running efficiently is the most important thing, because all the cogs fall into disuse and ruin if it breaks down.
A neutral creature recognizes it's a part of a society and/or ecosystem, and it respects that. It has concerns of its own as well, and those may well be put ahead of the welfare of the system, depending on the weight of the opposing needs. Goods must be paid for, but the children are hungry, it might risk stealing a chicken and some veg from a farm. The neighbor's wife is pretty hot and they've been fighting lately, but adulterers aren't looked at too fondly around the village, guess the ostracism isn't worth a few nights of fun. One balances the needs of the many with the needs of the self, so it's easiest to just casually go with the flow and try to reduce such tricky judgment calls to a minimum.
A chaotic creature isn't an island, but it might like to be. It has few expectations of the creatures and systems around it, and feels little or no obligation to them in turn. Such a creature need not be selfish, but it is self-centered, tending to see connections as transitory and circumstantial. Personal responsibility tends to be strong with these creatures, because Self is the only one they can reliably depend on. Whereas a neutral problem-solver might say "something must be done," and a lawful one would check into who is supposed to be doing what exactly, "I must do something" is the rallying cry of the chaotic creature faced with a problem. A chaotic creature need not be antisocial, but little regard for personal or business relationships may make it difficult for such an individual to keep friends and partners.