When Jon Snow returns to Castle Black after infiltrating the Free Folk, he is questioned by 5 of the Night's Watch, including Maester Aemon Targaryen.
After Maester Aemon dismisses Jon Snow saying they won't cut off his head today, Ser Alliser Thorne has a short curt conversation with Maester Aemon.
Thorne: I am acting commander here, Maester Aemon.
Aemon: Yes, you are.
Thorne: I don't trust the bastard.
Aemon: He told the truth.
Thorne: You always know when a man is telling a lie. How did you acquire this magical power?
Aemon: I grew up in King's Landing.
Merely growing up in King's Landing is not enough to detect liars, or else people like Jaime Lannister, Cersei Lannister, Margery Tyrell, Petyr Baelish, Olenna Tyrell, Maester Pycelle, and many others never would have gotten away with their lies.
Is there anything from the books or other canon sources that hint how Maester Aemon Targaryen became so skilled at detecting liars?
There is a place in Braavos where acolytes are trained to detect lies, but as far as I know, he never trained there.