I may be wrong, but isn't connecting to a web server by lynx illegal (considered "hacking") in some countries? I remember a case in the UK around the time of the London olympic games.
Lawyers will make the most egregious leaps and grasps to paint the opposing party in the worst light possible, especially in the early stages of the case, because if they don't claim that Lynx is a "hacker's tool" in the initial pleadings, then it may be looked upon with suspicion if they try to raise that point later. So they are essentially trying to reserve as many potentially beneficial claims as they can at once, including (and especially) any claim that may portend that the other party is a devious scoundrel with the worst possible intentions.
Lawyers will thus front-load with every kind of tenuous, ridiculous accusation they can (without presenting a significant risk to the licensing), expecting some of it to get "laughed out of court", just so that on the off chance that it doesn't, it will help their case.
I'm sure a real lawyer would contest that to some extent, and I'm sure there is slightly more nuance to it than that, but that is my layman's assessment and I think it is roughly accurate.
The takeaway is not to take legal pleadings too seriously, because the goal is not to find justice per se. It is for your side to win, to get what it wants, under the assumption that that automatically represents justice.
I believe, the case is part of a more general theme (which is, indeed, related to the EME topic): There's a perceptible will to regulate any kind of browsing into consumer-style app usage. E.g., manually entering a URL ("URL hacking") has been considered a fraud attempt; using a browser which only supports the basic protocol set and not all of it is considered as possibly related to intrusion and terrorism (oh, that T-word again). In the end, we may wake up with the law enforcing a certain, standardized life style. We may wake up with a deregulated companies and strictly regulated citizens.
This is not to say there aren't ridiculous prosecutions that run their course, especially in niche areas that aren't widely understood and thus hard to create public outcry over, like insider trading or computer crimes. It's just to indicate that using Lynx, by itself, is not considered criminal by any sane person. It's a nit the prosecutors pick when they're trying to nail you on something larger, a detail they exaggerate to attempt to create the impression of one's villainous ways.
Just don't want people to uninstall Lynx in fear that they'll be arrested for firing it up. :)
EDIT: From re-reading your comment, it seems you're suggesting that this wasn't part of a larger operation, but that actual charges were brought because of a single aberrant entry in the access logs? I find this hard to imagine, but if true, I would guess that this is more along the lines of "abuse of police power to harass an enemy" than "literally a random dude who just visited our site in a text-based browser". I've read access logs for many years now and even small sites get all kinds of weird things in there, it doesn't seem plausible that something like that would flag off any kind of detector. Do you have a link to more details about the case?
Basically anyone that can use a text based browser also is using some form of *nix and knows how to handle a command line application. They probably tinker with computers and so have many low level tools at their disposal.
Consider the difference carrying a knife, being a hunter, and carrying a knife being a bankrobber and going into a bank to use it.
Since illegality is, literally, whatever is contrary to the law, anything at all can be illegal. We can hope that crazy things won't be illegal, and decry their illegality—but, since it's convenient for a government to impose sufficiently many laws that anyone can have some infraction pinned on him or her (https://www.youtube.com/watch?v=JwsLAqjqnxo), to say that any particular thing can't be illegal is probably wishful thinking.