Should misleading advertisement be illegal in a libertarian society? Where should we draw the limit?
If it is a lie. If they lie about their product, it’s fraud.
Should lying be illegal?
Yes, lying is fraud but punishment for the fraud would vary depending on the damage that is caused because of it. If a company is selling a product that supposably has health benefits and it ends up hurting the public then they should be liable for the damage they caused and refunding customers that purchased it. If a company is selling long lasting light bulbs that do not work out of the box, the company would owe customers their money back and money for time wasted or a replacement light bulb that works as advertised. Notice how the punishment reflects the damage caused from the fraud.
if lying is a crime, does this mean libertarians oppose religious schools?
Lying should not be illegal. If I say you’re a moron, I’m free to do it (didn’t try to offend!). What I can’t do is lie about a good I’m offering, because that’s fraud.
Oh, no, you’re getting it wrong! 
Lying is not a crime, and religious schools would be welcomed in a libertarian society.
Lying about a product, claiming it has features it does not, is fraud. Religious schools advertise what they are going to teach your children, and proceed to do just that. If you don’t believe in X and Y, why would send your child to a school that outright tells you, “We teach X and Y.”? Where’s the fraud?
Lying, no. Fraud, yes. It all has to do with contracts and property exchange. If I walk up to you and tell you that New York City is in Mexico, when every reasonable person knows that New York City is in fact not in Mexico, then I have lied to you. However, because there was no contract or property exchange between us I have not committed any earthly crime. You simply go about your day with the knowledge that I am either an idiot or a liar.
Now, imagine that I am running a lemonade stand and the sign on my stand says that my lemonade is made from scratch with real lemons right there on the premises. You buy a cup of lemonade from me and then notice that I’m making the lemonade by simply mixing a concentrated powder and water. That’s fraud. We engaged in a voluntary property transfer under fraudulent terms because I advertised falsely. You have the right to restitution in this case.
Like promising eternal life in Heaven?
I think JackCuyler did a good job in explaining this. If a private school advertises that they teach according to the Bible which would mean teaching those who believe in Christ shall go to heaven and those who don’t will go to hell are not committing a crime because students are getting exactly what they payed for.
in religious sectors it’s still a choice to believe or not believe. you can walk away. if the religion doesn’t let a person walk away, then that’s initiating coercion. Which “promises to eternal…” do you know of that currently initiate coercion upon their congregetion if any individual in the congregetion would so happen to choose to leave (and anything tied to the state would merely be another instance in which the state is backing the coercion as in current fascist, socialist, and mercantilist methods)?
That one was actually good! OK, I don’t offer eternal life in Heaven. Also, none of the churches I know do, they just say “if you believe in X, you will live in Heaven for eternity”. OK, they can say that, but it would be wrong for them to say “if you believe in X and pay us a 1000 dollars, you will live in Heaven for eternity”. That MAY be a fraud, just I don’t know how to prove it.
Nevertheless, I don’t consider that much as a fraud. It’s a stupids trap. Fraud is when you offer a good (a Ferrari) and sell something different (an old car).
Religious advertisement does not deserve more respect than any other advertisement. If you’re promising pussy in the afterlife to those who join your sect, that’s fraud. The burden of proof is on the leader of the sect.
And I hope you’re familiar with the penalty for apostasy in Islam?
So it’s ok to promise people life in the afterlife as long as you don’t expect your followers to pay for it, right? Charging people and promising them that they will escape purgatory - as used to be common practice in the catholic church - will be considered a fraud, right?
Um, ask the cult leader to prove it. Caveat emptor. If you don’t, it’s your fault in this case…
Fraud and lying both imply a purposeful attempt to deceive. If a doctor makes a wrong diagnosis, it’s neither fraud nor lying, it’s incompetance at most.
That MAY be considered fraud. I think that’s the most difficult case, but I don’t care much, really. It’s not a fraud concerning an economic good.
Can you prove he was lying?
Isn’t life extending an economic good? I would put it on the same shelf as health care.