Well, for starters, IMO just because you're LG doesn't necessarily mean you can't be a mean angry cuss from time to time. I'd pretty much consider myself to be LG and I like to think that I can give some pretty menacing looks now and then.
Intimidation doesn't have to be about overt threats, or suggestions of physical harm. The Intimidation could just represent the intensity of the character- his ability to get a sense of urgency across to others.
Alternatively, as a LG character, you could have your Intimidation represent telling the criminal what sort of punishments are in store for him for breaking the law. No malice or viciousness behind informing him, but letting him know that he's going to the stocks for his crime, or will be subject to flogging or something if he doesn't come clean.
Basically, a good cop approach. "Look- I'm on your side here. If you cooperate with us, I'll make sure to put in a good word for you, get your sentence reduced."