I got lucky too. First adventure.
I got mine on the second, but didn't know if that's because I had already sent one out for the barracks quest line and before this new update appeared. If that's the case, then it happened on the first adventure after the new update.
Unfortunately, it took 6 adventures to get the scroll...thank goodness for the barracks! I think 6 is more than a few!
I actually got mine before I started the quest! I sent my knights out on the Dark Caves adventure for the barracks quest line then, on the same day, got as far as the Dark Caves part of this update. I thought I'd have to send the knights out again for the scroll so was amazed when they brought it back the next morning! Bizarrely, it meant I had the 'find the library scroll' part checked off before the 'go to the Dark Caves' part!! Needless to say, my knights got extra rations that day! Lucky, yes, but I did have to go on the desert adventure for over three weeks for my burning ember so I guess it was my turn for a bit of good fortune!
Just about to send my knights on the 3rd try,nothing so far.