but if he told the truth, and he's a liar, then he's lying, but then he would be lying about lying, so he's telling the truth, but he would lie about telling the truth, etc
no, he is a liar he/she just didn't lie that time but he/she is still a liar even though he said that's he's/shes a liar. So that means Some-random is wrong. I'm sorry but he's/shes a liar