A "line" is a sort of pre-rehearsed sentence, usually used to trick or manipulate someone else.
"What's a nice girl like you doing in a place like this?" is a classic pick-up line. (A pick-up line is something used to start a conversation with someone you're romantically interested in, usually in a bar or club.)
Jokes have punch lines - that's the last sentence at the end of the joke that delivers the laugh. "But now it's eating my popcorn!"
Actors must memorize their "lines" in a play.
So in your example "stupid lines" are the insincere statements, or lies really, that the speaker knows to be untrue.