Where does the idea that lightsabers can cut through solid objects come from?

The capacity of a lightsaber to cut through pretty much anything was firmly established in the novelisation of A New Hope (titled Star Wars: From the Adventures of Luke Skywalker), published more than 6 months before the film's theatrical release. There are multiple reference to it being more than a mere sword.

He knew what a lightsaber could do, though he had never seen one before. It could drill a hole right through the rock wall of Kenobi’s cave—or through a human being.

and

In between the start of his yell and the conclusion of the blink, the rodent-thing had been cleft cleanly down the middle, its two halves falling in opposite directions. The giant multiocular creature still stood staring, dazed, at the old human who was poised motionless before it, the shining lightsaber held over his head in a peculiar fashion. The creature’s chrome pistol fired once, blowing a hole in the door. Then the torso peeled away as neatly as had the body of the rodent, its two cauterized sections falling in opposite directions to lie motionless on the cool stone.

In "Phantom Menace", Qui-Gon cuts through a blast door.

Qui-Gon Cutting Through Door

In "A New Hope" a light saber easily lops off an arm. Better example (because not flesh, else one might mention Wampas and TaunTauns) might be how In ESB Vaders lightsaber easily cuts trough a couple of pipes when Vader and Luke have the fight on the gantry in the big shaft in the center of Bespin (there are previously scenes were the lightsaber pierced things, but that's the best example of a clean cut in that scene). There is also the scene were Luke cuts open the door of an ATAT in the Hoth battle to throw in a grenade. So discounting limbs, I would say that this was established at the lastest in the Empire Strikes back.