Cecil’s remark in line“Lucy Honeychurch has no faults,” said Cecil, with grave sincerity is made in a tone of:

I believe A is the correct answer. Grave in the quote means serious and on topic; sincerity means that the speaker really is convinced of what he says, so that seems to be the best choice. The tone is convinced of Lucy's good qualities, so B (nothing neutral about the comment), C (there is no hint that he saying one thing but meaning another), D (he is not surprised that she is like this, he is simply saying what he believes), or E (he seems neither worn out or skeptical about her good qualities) could not be the right answers.

A