(Oxford English Dictionary)
off book, adv. and adj.   
Theatre and Film. In predicative use: (of an actor) performing without a script, having memorized his or her lines.
1981   Shakes. Q. 32 221/2   Proteus was like an actor practicing the role of lover and not yet off book.
1986   R. K. Bank in W. B. Durham Amer. Theatre Companies 517   For..failure to be off book by the last rehearsal..fines were imposed or dismissal could result.
1991   Los Angeles Times (Electronic ed.) 22 Sept.  He carried a script in a couple of scenes where Cap’n Andy carries a script in the story, but otherwise he was ‘off book’.
 
StageMilk 
Actor’s Dictionary
Written by StageMilk Team on May, 10th 2016 | Acting Dictionary Resources
(...)
Off-Book: is when you have learnt your lines, either for a scene or the whole play. If you are “off book” you don’t need your script when performing.
 
YouTube
Lin-Manuel Miranda Teaches You Broadway Slang | Vanity Fair
Vanity Fair
Nov 27, 2018
Vanity Fair cover star Lin-Manuel Miranda teaches you Broadway slang.
   
Vanity Fair
SLANG SCHOOL | SEASON 1 | EPISODE 35
Lin-Manuel Miranda Teaches You Broadway Slang
Vanity Fair cover star Lin-Manuel Miranda teaches you Broadway slang.
Released on 11/27/2018
Transcript
(...)
Off book, off book means you’ve memorized your lines.
I’m not always off book.
As a matter of fact when I mess up my lyrics,
particularly if it’s a show I wrote and I’m also in,
I get amazing looks from my fellow cast members.