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Exactly what are you talking about? Chapter and Verse please.

When he said that he would never deny Christ? I don't think that was a lie. I think he fully intended not to deny Christ.

What happened when the cock crowed the second time, what did Peter do?

"He went out and wept bitterly"

Matthew 26:

[69] Now Peter was sitting outside in the courtyard. And a maid came up to him, and said, "You also were with Jesus the Galilean."
[70] But he denied it before them all, saying, "I do not know what you mean."
[71] And when he went out to the porch, another maid saw him, and she said to the bystanders, "This man was with Jesus of Nazareth."
[72] And again he denied it with an oath, "I do not know the man."
[73] After a little while the bystanders came up and said to Peter, "Certainly you are also one of them, for your accent betrays you."
[74] Then he began to invoke a curse on himself and to swear, "I do not know the man." And immediately the cock crowed.
[75] And Peter remembered the saying of Jesus, "Before the cock crows, you will deny me three times." And he went out and wept bitterly.

A lie is a lie no matter his good intentions. Remember, he swore that he's never forsake Jesus.