what information did the letter reveal that Dr. Livesey would not like?

Dr. Livesey would not like the fact that everyone knows they're sailing in search of treasure.

The admirable fellow literally slaved in my interest, and so, I may say, did everyone in Bristol, as soon as they got wind of the port we sailed for--treasure, I mean.

"Redruth," said I, interrupting the letter, "Dr. Livesey will not like that. The squire has been talking, after all."