From Wood v. State (Tex. Ct. App. June 18):
During the punishment phase of appellant's trial [for aggravated assault with a deadly weapon], Sheriff David Halliburton testified that appellant had a tattoo on each eyelid. The word "Lying" was on one, and "Eyes" on the other. Appellant objected to the testimony stating that it was not relevant. The trial court overruled the objection. The State mentioned the tattoos in its closing argument on punishment, arguing that they showed appellant's lack of respect for society.
At the punishment phase of a criminal trial, evidence may be presented as to any matter that the court deems relevant to sentencing. [In Texas, sentencing, even in noncapital cases, is often done by a jury. -EV] ... The tattoos were ... used ... to show his disregard for the truth and his moral character. A person's tattoos can reflect his character and demonstrate a motive for his crime. Conner v. State, 67 S.W.3d 192, 201 (Tex. Crim. App. 2001). The trial court did not err in admitting evidence of appellant's tattoos....
I'm not sure whether "lying eyes" does indeed show a person's "lack of respect for society" in the sense of lack of respect for moral or legal norms (as opposed to a lack of respect for its conventions of what's attractive and what's repulsive or even disgusting). "Lying eyes" could mean eyes that deceive their owner. Or it could mean eyes of a liar (which in the song were actually the part of the body that revealed the lie). Yet even if it means the latter, I doubt that people who have such tattoos are really admitting to being any more prone to lying than the average person.
Still, the threshold for admissibility of evidence is generally pretty low, especially at sentencing, where the question isn't just what a person did but what sort of person he is overall. And it's for a jury to determine just how much a person's own statements -- including his tattoos -- say about his character; so the court probably got it right as a matter of the admissibility of evidence, though if I were a juror I wouldn't give it much weight.