Did Jabba let Leia sleep? Because when Luke enters, she appears to be be sleeping but I'm not sure if she's just lying down.
She's just lying down, as you can see from the attached video clip
According to the original script, Jabba is sleeping and Leia is "lying in front of him"
Jabba is asleep on his throne, with Leia lying in front of him. Salacious sits by Jabba's tail, watching it wriggle. Leia is now dressed in the skimpy costume of a dancing girl; a chain runs from a manacle/necklace at her throat to her new master, Jabba the Hutt. Threepio stands behind Jabba as Bib comes up to the gangster slug.
In the official George Lucas/ James Khan novelisation, Luke senses Leia's pain "immediately", suggesting that she is wide awake when he arrives;
The lieutenant and the Jedi Knight approached the throne. Luke saw Leia seated there, now, by Jabba’s belly. She was chained at the neck and dressed in the skimpy costume of a dancing girl. He could feel her pain immediately, from across the room - but he said nothing, didn’t even look at her, shut her anguish completely out of his mind. For he needed to focus his attention entirely on Jabba.
Actually, with all due respect for Richard, Jabba did let Leia sleep while she was at his palace. She just didn't happen to be sleeping during that particular scene in the film. During Boba Fett's short-story in Tales of the Bounty Hunters, Leia is sent to Fett's room by Jabba as a "gift," with the instructions "enjoy her." Fett, not being a rapist, allows Leia to sleep in his bed while he sleeps in a nearby chair.
That short-story is criminally underrated, by the way; everyone should check it out if given the opportunity. Fett's later direction is nothing like Keys Moran's brilliant characterisation. It is widely considered by other Star Wars authors to be the best Star Wars short-story. Yes, that includes Timothy Zahn's work.
Most likely, since in real life, sleep deprivation is deadly and there is no reason that it is any different in universe.
However, there is no canon reference for Leia sleeping. Everything found by Richard doesn't have her sleeping.
Why not? Perhaps because a sleeping Leia would make for a boring scene.
Jabba must have let her sleep during her days with him. Yes, I said days, because - there is substantial evidence to show that Leia spent at least one full day and two full nights with him. Said evidence includes the fact that her slave outfit fits her as neatly as if it were made in Hollywood - the modeling process of which would take time that simply couldn't happen in one night, but I digress. Coupled with that is the fact that Leia went from being disgusted at Jabba's repulsive appearance while wearing a full suit of armor and clothing, to immediately running to him on his throne and pushing herself up against him while in a state of undress (on the Sail Barge), without even flinching; that shows she had spent enough time with him to begin getting used to being close to him - something which could easily have come with sleeping very close to him. Ergo, when Luke arrives, Leia is quite relaxed and rested...because Jabba let her sleep beside him.