If you engage in lying, you're fabricating, prevaricating, or speaking falsely. You are deliberately deviating from the truth.
If lying is the act of telling a lie, then "lying through your teeth" is the act of telling a bold lie, even if you know your listener will immediately know you're lying. Descended from a line in a Marx Brothers film, "Who you gonna believe, me or your lying eyes?" is spoken (ironically) by someone who's been caught lying and, instead of admitting it, says the evidence is wrong, as well as the person who's looking right at it.