Domande riguardo a frasi esempio con, spiegazione d'utilizzo di "Lucknow"s

A: "(Actually,) I wasn't aware" means that the speaker didn't know whatever the person speaking to them said until now. Adding the word "actually" to the sentence changes the meaning slightly to be contrary to what the other person has said.
Example:
"Did you know that James ate the last slice of pizza?"
"No, I wasn't aware."
Example 2:
"James ate the last slice of pizza. You knew that, right?"
"Actually, I wasn't aware."

"You are in luck" just means that things have worked out in your favor.
Example:
"Do you have any pizza left?"
"You're in luck because I actually have only one piece of pizza left"