All evidence points to the werewolves of this universe being incapable of controlling their actions while wolf-ified, and mostly unable to remember what happened the next morning. Despite their heightened senses, there is no evidence that they can distinguish blood relatives, or that such a distinction would hold any value for them while in that state. It takes a huge effort for Gwen to break through to Wolfman Lawrence, and it doesn't take. Yet when young Lawrence stumbles on his wolfed-out father just after he's failed to recognize his wife and brutally murdered her - his father somehow avoids attacking him.
When I watched the movie I got the very strong impression that the werewolves are perfectly capable of distinguishing targets and controlling their actions. Evidence for this is given when John Talbot becomes a werewolf and kills his wife, but not his son. Later on he does kill one of his sons, quite intentionally. Everything we learn about John indicates that he positively delights in the rampant murder and destruction he can anonymously cause via his transformations. His son on the other hand only attacks certain kinds of people; those that he hates (the doctors who torture him in the asylum) and those who get in his way or are actively trying to kill him. At several points in the movie he runs away from people he could very easily have killed, such as the entire police blockade in London. At his worst Talbotís actions are that of an animal suffering extreme sensory overload, blindly lashing out at everything around him with no understanding. On the other end of the spectrum he displays both curiosity and restraint when he meets Gwen in the woods (on every other kill in the movie, neither werewolf has shown any hesitation whatsoever) and seems to have gained a measure of control over himself just before the hunting party show up. If anything, Talbotís werewolf side acts like the Hulk if the Hulk were a hairy wolf-thing that only transformed at the full moon. His father is more like the Abomination.
Even if Sir John was acting entirely on instinct, it's not implausible that he's spare Lawrence as a child, but not his adult son in a later encounter. An adult might seem to the Beast like a potential threat to be destroyed, whereas a child-victim would be targeted simply as prey. He'd already killed Lawrence's mom, ergo the Beast already had food.
Near the end when Aberline sends one of his men to warn Sir John that Lawrence is coming, he doesn't seem even remotely suspicious towards the old man himself. Despite the fact that he did hear that doctor describing Lawrence's 'ravings' about not only being a lycantrope himself but his father being one as well. Moreover, when Ben's murder (which started it all) happened, Lawrence was far away from Blackmore - sounds like a decent alibi. And in the weeks that follow Lawrence's escape from asylum a 'Hey, the guy's 'I'm a werewolf' delusion turned out to not be a delusion at all. What if the rest of his 'crazy talk' is also true?' thought never crosses Aberline's mind.