This sentence has some parts which are superfluous: 1. "which got me to open my eyes" Someone presented some facts to you, which made you aware that you had trusted the wrong information in the past. These facts "opened your eyes" (the words "got me to" are unnecessary). 2. After realising the true facts, you knew who was telling you the truth and "who was lying". The phrase "of the one" sounds unnatural. Instead, the phrase "who was" already implies "the one" telling a lie. Considering the two points above, the sentence can be re-written as: "He stated some facts that I didn't notice before, which [opened] my eyes and [made me] realize who was telling the truth [and] who was lying. I hope this helps.

I think a phrase that would fit better would be "out of the two, I knew who was lying" or "that opened my eyes, and I knew which was lying" because you're referring to more then one person, so there would be no "one" when comparing two, if that makes sense. The phrase itself seems pretty unnatural, I've never heard it before at least