I don't know the text of Malory as well as I know Chretien. I do know that the two Quests for the Holy Grail are close enough that I'd be surprised there was any sort of controversy over the Queste (the Lancelot Grail's Holy Grail volume) being the source for Malory's. And the same with the Morte--the last book of the LG.
The wikipedia entry on Le Morte D'Arthur (Malory's, not the last volume of the LG) says he also used some English sources, and also added his own stuff.
The question of Chretien's source, on the other hand, is, I'm pretty sure, still an open question.
Eyes may glaze over, here, so, be warned.
Chretien claimed in the introduction to "Lancelot, or, The Knight of the Cart" that he had his story from Marie de Champagne. I seem to recall he'd said she'd given him a book, but my translation, now I look at it, only says she'd given him the material. At the time he was writing, it was fashionable to claim that you had some ancient source--it gave your work authenticity and weight, the idea of being "original" wasn't valued the same way we tend to these days. So there's every possibility that there never was any such book. Add in the fact that this happens to be the first appearance of Lancelot--Chretien obviously did a lot of inventing.
But Chretien didn't make the story up--it's the abduction of Guenevere, and there are at least two older versions. Neither of them includes Lancelot, of course. Either or both might have been Chretien's source, but there's no way of knowing for sure. One is a Life of Gildas, and the other is actually only a carving in the wall--an archivolt, actually--of a church in Modena, so that one probably wasn't his source, exactly, but the artist obviously got the story from somewhere else.
Tanget time! The Modena Archivolt has no sign of Lancelot--but Gawain is there. And Gawain appears in Chretien's Lancelot. He attempts a rescue, but fails. It strikes me as likely that Gawain was the original hero of the story Chretien was working from. Interestingly, the same is true in Chretien's Perceval--Gawain is also out looking. Chretien never finished it, but in the later continuations and adapatations, including the version most commonly known now, Gawain fails. Sometimes miserably. There was a time when Gawain was the supreme knight, the model of courtesy and bravery, but as time went by he became less admired. In the Lancelot Grail, he's treated very badly.
(In a part of the intro that Steve cut, I said that most Arthurian enthusiasts I'd run into had a favorite knight. Mine happens to be Sir Gawain. So I have little patience with the way the author of the LG (and ultimately Malory) makes Gawain's courtesy a sign of corruption, a sign that he's too bound up with the world to recognize spiritual things. The Gawain of the LG is venal and vengeful, rather that courteous and brave. It's done partly to make Galahad--the invention of the LG author--look better.)
No one's ever found a source for the Grail story, either, beyond Chretien. But I wonder if he had a source, and if Gawain was originally the hero of that story? There's no way of knowing, really, but it's interesting to ponder. If the topic interests one, of course.