Answer: The correct adjective form for the sentence provided is "liveliest": "Barkley is the liveliest of the two pups".
Step-by-step explanation: The correct form is the superlative adjective "liveliest". A superlative adjective expresses the highest degree of a quality; therefore, it makes reference to an extreme quality of a person or thing in comparison with other people or things. In that way, as Barkley is being compared with another pup and the article "the" is preceding the blank, the adjective form that fills in the blank is "liveliest", which means the other pup is not as lively as Barkley.