This really depends on the casting director and what they have specified for that audition. If they have explicitly stated that the actors must be off book during the audition, you must learn all of the lines that they have given you.
Generally speaking, it is not necessary for you to have memorized a monologue or the entire script. You may think that it works to your advantage being off book, but this is not always the case. If you do not know your lines properly you are likely to stumble and give off a worse impression. Casting directors understand that all actors will learn their lines properly for the shoot and so it is not that important unless previously stated.
The most important thing to do during your audition is to deliver your lines in a conversational and fluent manner. This allows you to engage with your audience and makes your performance more realistic.
If you have not been told to be off book for your audition but feel confident in your memorization of the script, you do not need to use it. We would still recommend holding the script in your hand though. This gives you a safety net just in case you forget your lines under pressure. If you blank and cannot save yourself, you are unlikely to have impressed with your audition.