Hey...

I'm not sure, you'll be convinced...but...

Sleep is the only verb these two sentences are using.
so if you remove one of the clause, then...
The orator put most of the audience to sleep
and
which was uninterested in the lecture, to sleep
if we dont use which, the second sentence will not make any sense.

also if we dont use 'which', the sentence convey the meaning as - most of the audience was uninterested...

Which is also used to select only some from 'most of the audience' and use of who makes the sentence bit awkward.

If this can help.....

Manhattan corrected it well. The first sentence is wrong because it looks like the orator was uninterested in the lecture, and it is clear that most of the audience was uninterested.

You have to use which, to attach the clause and it's okay here because it is being used to refer not to people, but to the word audience, which is not a person. So it's fine. The word 'which' has to be there.