Sure, Needs.
What specific lie?
Generally, its been well established by interviews with classmates that he has lied about the nature of his drinking habits. Specifically, in his characterization of "boofed." And more importantly, he lied about the definition of "devil's triangle" as discussed here, and as documented by journalists covering hte story:
https://twitter.com/davidenrich/status/1045416955522535425He also lied about what was meant by "Renate Alumnius" with even his own lawyer contradicting his explanation.
His FOX News interview was largely panned because of the ridiculous portrait he painted of his High School years, and he mostly continued that farce yesterday. A few FBI interviews of ex-classmates should quickly reveal those lies.
All that said, while lying to Senators should be enough, I suspect that there are bigger reasons why Kavanaugh and his Republican handlers don't want the FBI investigation.
And there are signs (including in Trump's latest statements) that they will bail on their nominee before that investigation is forced on them.