I think that it is debatable whether "a lot of birds singing" is actually grammatical, but it's certainly idiomatic. In my school days it would have been red-inked, but it is now considered normal. And just a minor change can transform the answer, which is, perhaps, why baab thought D could be correct.
I hear ... birds' singing.
A. a little
C. a lot of
D. a great deal of
(Although I'm not suggesting that these grammatically correct sentences are all idiomatic English)