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Actors have to memorize their lines.
Literal
Actor [topic-は] lines [obj-を] memorize must-[must-なければならない].
台詞 ('dialogue, lines') is a specialized word for lines in a play/movie; it can also be read as セリフ in katakana. 暗記する ('memorize by heart') literally 'dark-record,' is more specific than 覚える for the act of learning something verbatim. A generic profession-statement with topic は.