Lawful has nothing to do with following the law. Following an internal personal code in a strict manner, as well as an orderly method of doing things is what makes one lawful.
I would define lawful as adhering to codes that exist beyond oneself. I am certain that many a chaotic neutral, neutral evil, chaotic evil character behaves in a way that adheres to a strict moral and/or behavioral standard that they set for themselves. Like "always look out for numero uno" or "it is my duty to eat the rude."
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OP, it sounds like your paladin is behaving just fine for LG. LG characters are not required to obey every law and in particular are allowed to break laws in order to avoid committing evil acts.
However, it is generally a good idea to have a quick chat with your GM about expectations for a paladin, as some have very different ideas about what constitutes correct behavior and that's a good thing to know going in, before you smite the LN Cleric of Asmodeus.
NewDM: As you can see, you're not going to get one answer on this. But if you REALLY want to explore different opinions, here is a little light reading.
Here, I can summarize.
People have very different ideas about alignment.
People have very different ideas about paladins and how they interact with alignment.
People are often very invested in these opinions.
You should talk to your GM to make sure you don't have any problems playing a paladin.
Well, evil dragons aren't evil for no reason.
If the dragon isn't doing anything how does anyone know it's there?
In any event, it is part of the Oath Against Wyrms Paladin's code to kill all evil dragons. In and of itself that is the reason. And following his code is a lawful (order) act.