In the Harry Potter films, Lucius Malfoy bears his wand inside his walking stick:
Does he also do this in the books? Is there any description of him doing so, or of either his wand or his stick, in any of the 7 books?
No, it wasn't in the books (based on text searches I did on ebooks for Malfoy, cane, Lucius)
Moreover, it is explicitly confirmed by the actor who played Malfoy (Jason Isaacs) that he was the one who came up with the concept and the design
“I complained after [film] four or five that I didn’t have my own wand. I invented and designed my cane, that had a wand in it. I’d try to steal it at the end of the film and they’d catch me,” (Interview with Jason Isaacs on Milling About at the Edinburgh Film Festival in Scotland, sourced here)
I asked for a walking stick, which [Chamber of Secrets director] Chris Columbus first thought was because I had something wrong with my leg. I explained I wanted it as an affectation so I can pull my wand out [of the cane].
("Harry Potter' Villains: Jason Isaacs explains how Alan Rickman and Daniel Radcliffe helped create Lucius Malfoy" by Entertainment Weekly)
He also discussed it in one of the making-of videos on extended Blu-Ray collection as well but I don't have a specific cite now.
As far as I can tell, there is no mention in the book of Lucius Malfoy using a walking stick at all, much less storing his wand in it. For example, when he is first introduced in Chamber of Secrets (chapter At Flourish and Blotts):
The man who followed could only be his [Draco’s] father. He had the same pale, pointed face and identical cold grey eyes. Mr Malfoy crossed the shop …
When he later appears at Hogwarts to hand Dumbledore his order of suspension (chapter Cornelius Fudge), the narrator mentions his clothes, but no stick:
Mr Lucius Malfoy strode into Hagrid’s hut, swathed in a long black travelling cloak, …
The wand is first mentioned in the chapter Dobby’s reward:
He got up, his face livid, and pulled out his wand, but Dobby raised a long threatening finger.
It’s not clear from that description where he kept it; however, much later, when he is persuaded to surrender his wand to Voldemort at the start of Deathly Hallows (chapter The Dark Lord ascending), he has it in his robes as known from other wizards. This scene also contains more details about the wand, but again, no walking stick is mentioned:
At her [Narcissa Malfoy’s] touch, Malfoy put his hand into his robes, withdrew a wand and passed it along to Voldemort, who held it up in front of his red eyes, examining it closely.
‘What is it?’
‘Elm, my Lord,’ whispered Malfoy.
‘And the core?’
‘Dragon – dragon heartstring.’