Why would Flynn lie to Pence?
Here is a plausible -- and I would venture "probable" -- explanation.
Unlike Pence, Trump and Russia's kleptocratic thug-murderer-enemy-of-the-United States participate in the world's best known "Mutual Admiration Society."
If, as I suppose, Trump is compromised in his relationship with Putin -- it could be nothing "more" than Putin's knowledge that Trump is in deep debt to Russian bankers -- then America's "Manchurian Candidate" would need an "undercover go-between" to communicate with KT (Kleptocratic Thug).
However, it would also be necessary for Trump to conduct these conversations with someone powerful enough to act in his stead so that MC (Manchurian Candidate) could maintain plausible deniability when asked about communication with Putin. "No, since taking office, I have had no other interaction with Mr. Putin except for my public record phone call with him."
However, "plausible deniability" works best when no additional confidantes are "let in" on "the secret" - especially someone like Pence who would become president if he leaked information that resulted in Devious Donald's impeachment.
And so Pence -- a straight-arrow "Christian" "conservative," born and raised in America's "Heartland" -- had to be kept in the dark.
Learn more about "plausible deniability" at the following Wikipedia page.