I was looking at this interactive map of Middle-earth, and noticed that when you click on the node at Isengard, one of the dates says:
The Black Riders visit Saruman who lies that Gandalf has "confessed", and gives them directions to the Shire.
(emphasis mine)
Why did he lie? My best guess is that he didn't want Sauron to know that Gandalf had escaped, but surely Sauron would find out at some point?
The note seems to come from a quote in the Unfinished Tales in a section titled "Other Versions of the Story" in the chapter "The Hunt for the Ring". The quote is as follows:
He went back to the Gate, and he lied, saying that he had made Gandalf confess. He did not admit that this was his own knowledge, not being aware of how much Sauron knew of his mind and heart.
Unfinished Tales: Part Three: The Third Age, IV: The Hunt for the Ring, Other Versions of the Story
To provide context for the quote. The version of the story it comes from is labelled "Version C", in which (unlike A and B) Gandalf is still a prisoner at the time of the Nazgûl arriving at the gates of Orthanc. In C, Saruman is prepared to yield to Gandalf and beg for his help as he perceives the full horror of being in service to the Dark Tower. Saruman tells the Nazgûl "that he would go and try to discover what he knew; if that were unavailing, he would deliver Gandalf up to them." However, upon is return to the top of Orthanc, Saruman discovers Gandalf has escaped.
Saruman's lie seems to come as a combination of not wanting Sauron to know that he has lost Gandalf, not wanting Sauron to know that he was aware of the whereabouts of the Shire and searching for the Ring himself, and not wanting Sauron to know that he was willing to forgo service to him in exchange for aid from Gandalf.
The above quote comes with the following note:
Earlier in this version it is said that Sauron had at this time, by means of the palantíri, at last begun to daunt Saruman, and could in any case often read his thought even when he withheld information. Thus Sauron was aware that Saruman had some guess at the place where the Ring was; and Saruman actually revealed that he had got as his prisoner Gandalf, who knew the most.
ibid.
The note isn't overly informative but tells us that whatever lies Saruman tells it is most likely that through the palantíri Sauron can perceive the truth.
In fact it is, again unlike A and B, not Gríma who reveals Saruman's lies but a Dunlending spy of Saruman's:
This Dunlending was overtaken by several of the Black Riders as they approached the Tharbad crossing. In an extremity of terror he was haled to the Witch-king and questioned. He saved his life by betraying Saruman. The Witch-king thus learned that Saruman knew well all along where the Shire was, and knew much about it, which he could and should have told to Sauron’s servants if he had been a true ally.
ibid.
Saruman wanted to work together with Sauron, at least until he could get his hands on the One Ring, when he would ditch Sauron.
Saruman's first mission from Sauron is to capture Gandalf and remove him as an obstacle, by either killing him, imprisoning him or making him join the cause with Sauron. Gandalf escaping goes against that mission, makes Saruman look like a failure and might give Sauron certain... ideas. Ideas Saruman doesn't want him to have.
