In this example that is exactly what this means! To deliver a line means to say something that has been prepared. Usually this references actors and actresses. For example, "Daniel Radcliffe delivered his lines as Harry Potter very convincingly". I hope this helps.

It sounds like you mean -to give a line- ( to lead on or to deceive with false talk ) to deliver a line ( is to recite a script )

Just adding to what's already been said here, when used specifically in the context of speech, "deliver" can have a more general meaning than prepared speech, and can simply mean you say something that is aimed at a particular person or audience (you "deliver" it to that person/those people). You might compliment someone on their "excellent delivery" of a speech, for example. The meaning of the word isn't connected with the idea of persuasion.