Final answer:
The work in question is Lord Byron's satirical poem 'Don Juan', which is considered his masterpiece with the first two cantos being published in 1819.
Step-by-step explanation:
The first two cantos of Lord Byron's poem that are considered his masterpiece were first published in 1819. This work is none other than the famous satirical poem Don Juan, which showcases Byron's distinctive style and flair for storytelling. Don Juan is particularly known for its use of various rhyming patterns, including half rhyme/eye rhyme and double rhymes as seen in his widely recognized opening stanza.