Okay, a large number of the great heroes would be considered Lawful Good.
Superman is the prime example, with his Truth, Justice, and the American way thing.
Batman is another example, in my opinion. Even though he operates in the shadows, it is because it is there that evil and corruption is found. Batman also has a strong personal code and a strong sense of justice and order.
If the character is not yet as capable as a superhero and the challenges he faces great, he may or may not have the courage to face them. But he will still have his feelings about what is right and good, and if the opportunity arises, he will act on them.
That said, the LG character is the most likely to take action for reasons of alignment, as acting in the behalf of good and law are more tangible goals than acting for the sake of chaos, neutrality, or evil.
Just have your character act in a way that you feel is moral and just, and you'll do fine.