Joe, while you're dead balls on with your principles and attitude of such a person, you're not thinking this through completely.
I'm a firm believer in doing things not just for the principle, but also for the best possible outcome. While you might be 100% in the right, it still takes time and money if you just say.... Wanna sue me ?? Go right ahead and I'll prove you wrong in a court of law and you'll pay my lawyer's fees and court costs, to boot. It's very hard to get someone to pay all of your costs.... even if you're in the right. Besides, you won't get lost wages for all the preparation, meeting with your attorney or your time going, sitting and coming back from the case itself. Lotta wasted time and money on one's part to prove a point.
A quick meeting, a short piece of written paper or whatever before taking a stand of 'You're a crazy lady and I'll prove it in court'. Judges don't care much if you're in the right or not, but frivolous lawsuits are really frowned upon by almost all courts, except for Judge Judy's courtroom, where she thrives on this kinda nonsense. The general consensus of judges is hopefully one party will have enough sense of how to thwart this kinda BS from reaching a courtroom.
The fastest way from point 'A' to point 'B' is a straight line and that's a direct conversation with the nutjob in question and get it over-with in person. Take one or two trustworthy witnesses along, if you're scared.
No you see I'm thinking it through very clearly. And principal has less to do with it than simple common sense. Until an actual lawyer contacts you, it's just a baseless threat by someone who wants something from you for nothing.
So you have a few possible outcomes here, (I'll put them in what I believe is most likely to least likely)
1.Person threatens to sue you. You call their bluff, you don't waste any time or money dealing with it. They go away. This is your best outcome because they didn't get what they want through dishonest means and you didn't waste any resources dealing with it.
2.Person threatens to sue you. Their lawyer does get involved. Lawyer recognizes this person has no case, advises them to drop it. You have wasted none of your time or efforts. Still a good outcome for you.
3.Person threatens to sue you, Their lawyer gets involved, Their lawyer contacts you. You don't meet with them directly but contact your lawyer and have them take care of it. In this case at least you are protected, but it will cost you some. However maybe not as much as it would to fix this persons sign for free or discounted price.
4.Person threatens to sue you. You waste your time having a meeting with them. The unreasonable person doesn't like what you have to say and still threatens to sue you. You call their bluff. You don't waste any additional time or money dealing with it, even though you did waste time at the meeting and preparing for the meeting. They go away.
5.Person threatens to sue you. You waste your time having a meeting with them. The unreasonable person doesn't like what you have to say and still threatens to sue you. Their lawyer does get involved, Lawyer recognizes this person has no case, advises them to drop it.
6.Person threatens to sue you. You waste your time having a meeting with them. The unreasonable person doesn't like what you have to say and still threatens to sue you. Their lawyer gets involved. Their lawyer contacts you. You don't meet with them directly but contact your lawyer deal with them and have them take care of it. In this case you aren't as protected before because you may potentially provided the other person and his or her lawyer with ammunition during your initial meeting. Also now their lawyer knows your hand. and it will cost you some because now your lawyer has more work to do to protect you.
7. Person threatens to sue you. You waste your time having a meeting with them, The only way you can please them is by offering them some sort of deal, which leads to more work, This person continues to be unreasonable to work with and you lose more money, and they get free or discounted services. Heck they may threaten to sue you again for something else.
8. Person threatens to sue you. You waste your time having a meeting with them, The only way you can please them is by offering them some sort of deal, which leads to more work, They are then easy to work with, but you are still doing work for a discounted rate, so you are loosing money.
9. Person threatens to sue you. In your meeting the person listens to reason but still sin't happy that they didn't get some sort of deal. They don't hire you, You go on with your life.
10. Person threatens to sue you. The meeting goes well and the person listens to reason, and hires you to fix their sign at normal rate(s).
11. Person threatens to sue you. It does go to court, you win. You wasted some time, maybe some money depending on if you or they would have to pay court and lawyer fees.
12. Person threatens to sue you. It does go to court, you somehow loose. That's bad but it sounds unlikely in this case.
13. Person threatens to sue you. You have a meeting with them. During the meeting you find out this person is your soul mate, you ask her to marry you right then an there. You move in together, for several months everything is great, then you look on the fridge at the "honey do" list and it says "fix my sign" You fix the sign, the person then divorces you takes everything you own, and now has a brand new sign.
So as you can see a lot of different things COULD happen. But I would be willing to bet that they wont sue. Keep in mind there are factors we do know that we can use to make a good decision anytime we are dealing with risk vs reward. This person is being unreasonable. We know this already. Spending time on anything without being paid costs us money. Spending time on anything and getting paid a fraction of what you would normally charge, would still result in the loss of money. (unless you haven't any work). The other person is conscious of the fact that Hiring a lawyer or going to court will likely cost them money. Lawyers LOVE to win and typically advice their clients on their chances of winning a case, and in most cases will attempt to talk a client out of situation where they are sure to lose.
So as you can see claiming that I am not "thinking this through completely" is not accurate at all. In fact it's flat out wrong. I like to consider possibilities and likelihoods. You may disagree with my conclusion, but to claim it is devoid of thought and based on principal or attitude is simply untrue. Based on what we know, I would challenge where your head is at, since you called mine into question.
) name. I consider all dealings with clients as business "relationship", this is why I chose that word. I'm pretty sure I'm not the only one who has used that word in that way. So all of that is beside the point. This "relationship" didn't start with the person in question hiring 401 to make her sign. It started with a threat, and I'm going to take 401's word for it when he says he did not harm her sign, so it would be a baseless threat on her part. Meaning the person in question is dishonest in her attempt to have 401 solve HER problem by claiming that he caused the problem at which point she then threatening to harm his business with legal action. 
