The quote about the kingdom of Awadh being "a cherry that will drop into our mouth one day" is attributed to Lord Dalhousie. This statement reflects the imperialistic approach and expansionist policies of Lord Dalhousie during his tenure as Governor-General of India from 1848 to 1856. Lord Dalhousie was known for the Doctrine of Lapse, a policy that allowed the British East India Company to annex states where the ruler had no natural heir or adopted heir. Awadh (Oudh) faced annexation under this policy in 1856. The quote signifies the perception that Awadh was a desirable and strategically important region that the British sought to annex as part of their territorial expansion in India.

So, the correct option is [2].