The nature of Nathan Radley's character betrays a degree of weirdness and unfriendliness toward the children that leaves us no choice but to not take anything he says to them at face value. That being said, it is more than likely he was lying about the reason why he poured cement in the knothole of the tree, which served as the primary medium of unspoken communication between Boo and the kids. Leaving "gifts" for the kids was tantamount to making contact with the outside world. Other than that, his brother, Nathan, keeps him inside the house, perhaps as a way to protect him but potentially as a way to control him. We never really know.
What we do know is that Nathan decided to eliminate the tree stump, thus eliminating the contact with the kids.
"I filled it up."
"Why'd you do it, sir?"
"Tree's dying. You plug 'em with cement when they're sick. You ought to know that, Jem." (Ch. 7)
Whatever his reasons truly were, there is nothing in the annals of any field or study on common knowledge that has ever indicated that you plug a knothole with cement when a tree is sick.
In Chapter 7, Jem and Scout write a thank you note to the anonymous individual who has been leaving them gifts in the knothole of the Radley tree. When Jem runs out to put the note inside the tree, he discovers that the knothole has been filled in with cement. Jem then patiently waits for Nathan Radley to arrive the next day and asks Nathan if he put cement in the knothole of the tree. Nathan tells Jem that he put the cement in the tree because it was dying. Nathan said,
"You plug 'em with cement when they're sick" (Lee 39).
Later that day, Jem asks Atticus if he thinks the tree is dying. When Atticus tells Jem that the tree looks healthy, Jem realizes that Nathan Radley lied to him. In my opinion, Nathan Radley told Jem a lie and the real reason as to why he put cement in the knothole was to stop Boo from communicating with the children.
This happens in Chapter 7 of the book. When Nathan Radley fills the knot hole in the tree with cement, he says that it is because the tree is sick.
I really do not believe that Mr. Radley is telling the truth when he says that he did it because the tree was sick. Cement would not be very likely to help a tree stop being sick. In addition, Atticus tells Jem that the tree was not sick. Instead, I believe that Nathan does it because he does not want Boo to keep leaving gifts for the kids -- just out of meanness, really.
Nathan Radley in "To Kill a Mockingbird" became like his father. His father was anti-social and kept the boys and his wife confined to the home. Scout and Jem said that Mr. Radley was the only one who went to town. It was a known fact in the town that Boo was kept secluded. The townspeople thought when Mr. Radley died that they would finally get to see Boo after not having seen him for so many years. However, it did not happen. Nathan took over and continued the same lifestyle as his father.
No, I don't believe that Nathan told the truth. He may have felt that Boo could get accused of something if he kept trying to communicate with the children. It could have been his way of protecting his brother.