According to "Does the center hold?" by Donald D. Palmer, Socrates's main argument during his trial was that "he knew nothing". But Socrates discussed various topics with many people, he had knowledge in many areas. Can we then consider him a liar?
Not to dispute Dr. Palmer's account, but Socrates' main argument at his trial was that he was not trying to impose knowledge on the citizens of Athens. Instead — to use Socrates' analogy — he was like a horse-fly, biting at their presumptions and assumptions and forcing them out of the complacent drowsiness of mere 'knowledge' into philosophical engagement with their own beliefs and understandings. He was pushing the people of Athens to think for themselves, not trying to get them to listen to his ideas, and thus he could not rightfully be accused of corrupting anyone.
We might accuse Socrates of being a pain in the you-know-what — and it appears he would gladly agree with us — but I don't think it's correct to accuse him of lying.
Socrates might not have ever claimed this.
See here. An example of what he did say is:
I am wiser than this man, for neither of us appears to know anything great and good; but he fancies he knows something, although he knows nothing; whereas I, as I do not know anything, so I do not fancy I do. In this trifling particular, then, I appear to be wiser than he, because I do not fancy I know what I do not know.
Socrates is saying here that he does not know anything great and good, not that he does not know anything at all.
In context here. He goes on to describe that craftsmen do have knowledge.
And in this I was not deceived; they did know what I did not, and in this way they were wiser than I. But, men of Athens, the good artisans also seemed to me to have the same failing as the poets; because of practicing his art well, each one thought he was very wise in the other most important matters, and this folly of theirs obscured that wisdom
Socrates is not denying the possibility of knowledge held by others, nor is he saying he holds no knowledge. He is simply saying no one has certainty on the big questions (such as politics and justice), and he thinks he is better because he acknowledges this.
You stumbled over the Socratic paradox.
It is a classical example of the Dunning–Kruger effect: You need a certain minimal competence to begin to perceive your own degree of incompetence.
Because reality is arguably infinitely complex chances are that any increase in competence only increases the insight into the vastness of our incompetence. Socrates, surely one of the brightest and smartest, was simply more aware of it than most of us.
It is only consequent that his preferred way of teaching was the Socratic method: He did not disseminate ready-made truths but ironically challenged what others thought was evident.